geometry l1 2015 final review informational packet unit objectives · 2017-05-23 · 10. prove...

GEOMETRY L1 2015 FINAL REVIEW INFORMATIONAL PACKET

UNIT OBJECTIVES UNIT 1 – BASICS OF GEOMETRY

1. Identify and apply the three undefined terms; points, lines and planes. 2. Use the undefined terms to define segments, angles, rays, bisector. 3. Name and classify angles as acute, right, obtuse. 4. Identify angle pairs and find measures; adjacent, vertical, supplementary, complementary using algebraic (linear, quadratic) methods 5. Apply formulas for perimeter, area and circumference. 6. Develop and apply the formula for midpoint. 7. Use the distance formula and Pythagorean Theorem to find the distance between two points on a coordinate plane. 8. Identify reflections, rotations and translations of points, lines, segments and angles. UNIT 2 – REASONING & PROOF 1. Use inductive reasoning to identify patterns and make conjectures. 2. Find counterexamples to disprove conjectures. 3. Identify, write and analyze the truth value of conditional statements converse, inverse and contrapositive of conditional statements. 4. Write an analyze bi-conditional statements. 5. Identify properties of equality and congruence and use them to write algebraic proofs and geometric proofs. 6. Write two-column proofs. 7. Prove geometric theorems by using deductive reasoning. UNIT 3 – PARALLEL & PERPENDICULAR LINES 1. Identify parallel, perpendicular and skew lines. 2. Construct parallel, perpendicular and skew lines. 3. Prove and apply theorems about perpendicular lines. 4. Identify the angles formed by two lines and a transversal. 5. Prove and use theorems about the angles formed by parallel lines and a transversal. 6. Use the angles formed by a transversal to prove 2 lines parallel. 7. Use slope to identify parallel and perpendicular lines. 8. Write equations of parallel and perpendicular lines. 9. Classify lines as parallel, intersecting or coinciding on coordinate plane.

UNIT 4 – CONGRUENT TRIANGLES 1. Classifying triangles by angle measure and sides length. 2. Use triangle classification to find angle measure and side length. (Include linear and quadratic expressions) 3. Use properties of congruent triangles. 4. Prove triangles congruent by using the definition of congruence. 5. Apply SSS, SAS and ASA to solve problems and prove triangles congruent. 6. Use CPCTC to prove parts of triangles congruent. 7. Draw, identify and describe transformations of triangles in a coordinate plane. 8. Use properties of rigid motions to determine whether figures are congruent and to prove figures congruent. 9. Position figures in coordinate plane for use in coordinate proofs. 10. Prove geometric concepts by using coordinate proof. 11. Prove theorems and apply properties about isosceles and equilateral triangles. UNIT 5 – PROPERTIES OF TRIANGLES 1. Prove and apply theorems about perpendicular bisectors and angle bisectors. 2. Prove and apply properties of perpendicular bisectors, angle bisectors, medians, altitudes and midsegements. 3. Construct a perpendicular bisector of a segment, an angle bisector, the circumcenter and incenter of a triangle. 4. Use the Converse of Pythagorean Theorem to classify triangles. 5. Justify and apply properties of 45-45-90 and 30-60-90 right triangles. UNIT 6 – QUADRILATERALS 1. Find and use the measures of interior and exterior angles of polygons. 2. Prove and apply properties of parallelograms. 3. Use and apply properties of parallelograms to solve problems. 4. Prove that a given quadrilateral is a parallelogram. 5. Prove an apply properties of rhombi, rectangles and squares. 6. Use and apply properties of rhombi, rectangles and squares to solve problems. 7. Prove that a given quadrilateral is a rhombus, rectangle or a square. 8. Reflect, rotate and translate a parallelogram. UNIT 7 – SIMILARITY 1. Identify similar polygons. 2. Apply properties of similar polygons to solve problems. 3. Draw and describe similarity transformations in the coordinate plane. 4. Use properties of similarity transformations to determine whether polygons are similar and to prove circles are similar. 5. Use AA, SSS and SAS similarity criteria to determine if two triangles are similar. 6. Use properties of similar triangles to solve problems and find segment lengths by indirect measure. 7. Use properties of similar triangles to apply Triangle Angle Bisector Theorem and Triangle Proportionality Theorem. 8. Apply similar triangle properties to use dilation on coordinate plane.

UNIT 8 – RIGHT TRIANGLES 1. Use Geometric Mean to find segment lengths in right triangles. 2. Apply similarity relationships in right triangles to solve problems. 3. Find the sine, cosine and tangent of an acute angle. 4. Use trigonometric ratios to find side lengths and angle measures in right triangles and to solve real world problems including but not limited to angle of elevation, and of depression, height, distance away, etc. UNIT 9 – AREA 1. Use the area formula for a triangle to create the area formula for regular polygons. 2. Use right triangle relationships to help find the area of regular polygons. 3. Find the measure of a remote interior angle of a regular polygon. 4. Find the sum of the exterior angles of a regular polygon. 5. Calculate Geometric Probability. UNIT 10 – CIRCLES 1. Identify tangents, secants and chords and use their properties to solve problems. 2. Apply properties of arcs and chords. 3. Find the area of sectors. 4. Find arc lengths. 5. Find the measure of an inscribed angle and use their properties of solve problems. 6. Find the measures of angles and lengths of segments formed by lines that intersect circles. 7. Use the measures of angles and lengths of segments formed by lines that intersect circles to solve problems. 8. Write and graph the equation of a circle. 9. Use the equation of a circle to solve problems. UNIT 11 – 3 DIMENSIONAL FIGURES 1. Classify 3-dimensional figures according to their properties. 2. Use nets and cross-sections to analyze 3-dimensional figures. 3. Apply the formula for volume for prism, cylinder, pyramid, cone and sphere. 4. Use volume formula to solve real world problems.

GEOMETRY L1 2014 FINAL REVIEW INFORMATIONAL PACKET

UNIT VOCABULARY UNIT 1 – BASICS OF GEOMETRY

Undefined terms, point, line, plane, segment, ray, collinear, coplanar, intersect, distance, postulates, congruent, angle, sides, vertex, adjacent angles, acute, right, obtuse, midpoint, bisects, vertical angles, linear pair, supplementary, complementary, angle, area, coordinate plane, perimeter, transformation, dialation, isometry, translation, rotation, reflection, endpoint, pre-image, image UNIT 2 – REASONING & PROOF Conjecture, counterexample, deductive reasoning, inductive reasoning, proof, theorem, postulate, conditional statement, bi-conditional statement, conclusion, two-column proof UNIT 3 – PARALLEL & PERPENDICULAR LINES Parallel Lines, Skew Lines, Parallel Lines, Perpendicular Lines, Transversal, alternate exterior angles, alternate interior angles, corresponding angles, same-side interior angles (consecutive interior angles), coordinate plane, coordinates, slope, y-intercept UNIT 4 – CONGRUENT TRIANGLES Acute triangle, obtuse triangle, congruent, equilateral triangle, interior angle, exterior angle, isosceles triangle, right triangle, scalene triangle, corresponding angles, corresponding sides, base angles, vertex angle, bases, hypotenuse, legs, SSS, SAS, ASA, AAS, HL UNIT 5 – PROPERTIES OF TRIANGLES Altitude, perpendicular bisector, median, midsegment, angle bisector, concurrent, equidistant, orthocenter, centroid, incenter, circumcenter, point of concurrency UNIT 6 – QUADRILATERALS Quadrilateral, parallelogram, kite, square, rectangle, polygon, trapezoid, isosceles trapezoid, rhombus, exterior angle, equidistant, diagonals, opposite angles, opposite sides, consecutive angles, consecutive sides, concave, convex, regular UNIT 7 – SIMILARITY AA Similarity, corresponding angle, triangle proportionality theorem, ratio, proportion, similarity, dilation. UNIT 8 – RIGHT TRIANGLES Sine, cosine, tangent, SOHCAHTOA, hypotenuse, leg, right angle, geometric mean, altitude, angle of elevation, angle of depression, trig ratio, inverse functions, Pythagorean theorem

UNIT 9 – AREA Regular polygon, interior angle, exterior angle, apothem, radius, composite figure, geometric probability, perimeter, area, pentagon, hexagon, octagon, nonagon, decagon, n-gon UNIT 10 – CIRCLES Radius, diameter, chord, secant, tangent, central angle, inscribed angle, arc, major arc, minor arc, semicircle, concentric circles, exterior of a circle, interior of a circle, on the circle, point of tangency, sector, arc length, intercepted arc UNIT 11 – 3 DIMENSIONAL FIGURES Surface area, volume, cone, pyramid, prism, sphere, cylinder, polyhedron, radius, great circle, hemisphere, cube, edge, vertex

Name ________________________________________ Date ___________________ Class __________________

Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

Holt McDougal Geometry

Extending Perimeter, Circumference, and Area Chapter Test Form C

1. Express the area of an equilateral triangle in terms of the length s of a side.

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2. Find the area of the parallelogram.

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3. The longer diagonal of a rhombus is equal to 3 times one of its sides. The length of a side is 6 inches. Determine the area of the rhombus. Leave your answer in simplest radical form.

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4. The midsegment of the trapezoid has a length of 11.5 cm. Find the area of the trapezoid.

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5. Find the area of the kite.

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6. The area of an equilateral triangle is equal to the area of a trapezoid. The trapezoid has bases with lengths 4 centimeters and 14 centimeters and an altitude of 4 3 centimeters. Determine the perimeter of the triangle.

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7. A circle is circumscribed about a square. The square has side lengths of 8 inches. Find the circumference of the circle in terms of �. Leave your answer in simplest radical form.

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8. A regular hexagon is circumscribed about a circle. The circle has a radius of 9 feet. Find the area of the hexagon to the nearest tenth.

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9. Find the area of the square.

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Name ________________________________________ Date ___________________ Class __________________



Extending Perimeter, Circumference, and Area Chapter Test Form C continued

10.The radius of the circle circumscribed around the regular hexagon is 10 centimeters. Find the area of the shaded part of the figure to the nearest tenth.

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11. Sod is going to be placed over an irregularly shaped area. If sod costs $6 a square yard, estimate the cost of the sod needed to cover the area. The grid has squares with side lengths of 2 feet.

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12. Find the perimeter of the polygon with vertices A(�2, 3), B(1, 5), C(1, 0), and D(�2, �2). Round your answer to the nearest tenth.

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13. Find the area of a circle centered at (1, 1) that passes through the point (�2, 6). Round your answer to the nearest tenth.

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14. Find the area of the polygon with vertices D(4, 1), E(2, 4), F(�3, 2),and G(0, �4).

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15. Determine the effect on the area of a parallelogram if the height is multiplied by 3 and the base is multiplied by 6.

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16. A circle has a diameter of 5 feet. If the circumference is multiplied by (2x � 4), find the area of the new circle.

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17. A point is chosen randomly on .ADFind the probability the point is on BCor .CD

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18. A weather channel covers local weather 6 times per hour for a period of 2 minutes. If you turn to the weather channel 5 times, predict how often you will catch the local weather.

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Name Date Class



CirclesChapter Test Form C

1. Classify the lines and segments that intersect .A�

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2. Mount McKinley in Alaska is North America’s highest mountain. The distance from the summit to the horizon is about 176 miles. To the nearest tenth of a mile, find the height of the mountain.

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3. Given m�WVX � 45 and ,VW UX� find �m .UV

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4. Write True or False. Chords equally distant from the center of a circle are congruent.

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5. Find the area of the segment of the circle to the nearest hundredth.

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6. To the nearest degree, find the measure of the central angle for �JK if the length of �JK is 2.4 units and the radius is 6 units.

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7. Find m�LPO.

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8. Find m�RSP.

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Name Date Class



CirclesChapter Test Form C continued

9.If m�ACG � 65, m�AGC � 80, � � �m 100 ,DC � � �m 70 ,BC and

FA and GC are tangent to the circle, find m�AFD.

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10. Find m�TMU.

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11. Find �m .SPQ

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12. Find the length of .KL

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13. Find the length of .BD

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14. Find the diameter.

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15. Write an equation for the locus of all points in the coordinate plane that are 5 units from (3, 4).

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16. Graph a circle with a diameter of 4 units that is tangent to the line y � 2.

17. A hospital trauma center is going to be built equidistant from three cities. Positioned on a grid, the cities would be located at (3, �2), (�2, 3), and (�6, �5). What are the coordinates of the location where the trauma center should be built?

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Name ________________________________________ Date ___________________ Class __________________



Polygons and Quadrilaterals Chapter Test Form C

1. Identify the figure as specifically as possible.

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2. An interior angle of a regular convex polygon measures 144�. How many sides does the polygon have?

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3. The exterior angles of a convex pentagon measure (18x � 12)�, 16x�,(8x� 6)�, (10x � 12)�, and (5x � 12)�.Determine the measure of the largest interior angle.

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4. Three vertices of parallelogram PQRSare P(�1, 3), Q(4, 1), and R(1, �2).Find the coordinates of vertex S.

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5. Given � ,ABCD determine the valueof y.

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6. In � ,EFGH the diagonals intersect at Y.If EY � x2 and GY � 2x � 3, determine the length of EG .

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7. Prove that JKLM is a parallelogram.

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8. Use the definition of parallelogram to show that the quadrilateral with vertices A(�4, 4), B(�2, 0), C(6, 4), and D(4, 8) is a parallelogram.

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9. Give the best name for the quadrilateral with vertices (�2, 1), (�3, �2), (4, �1), and (3, �4).

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Name ________________________________________ Date ___________________ Class __________________



Polygons and Quadrilaterals Chapter Test Form C continued

10.Find the perimeter of a square if half of a diagonal is equal to 8 inches.

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11. Determine the value of x.

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12. Write True or False. If the midpoints of the sides of a parallelogram, when connected in order, form a rectangle, then the parallelogram is a rhombus.

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13. Use the diagonals to determine whether a parallelogram with vertices (�3, 2), (�1, 4), (8, �5), and (6, �7) is a rectangle, rhombus, or square.

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14. Give the best name for the quadrilateral with vertices (�1, 1), (1, 3), (3, 1), and(1, �3).

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15. Find the value of x so that ABCD is an isosceles trapezoid with bases AD and BC .

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16. XY is the midsegment of the trapezoid. Find the value of x.

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Name ________________________________________ Date ___________________ Class __________________



Right Triangles and Trigonometry Chapter Test Form C

1. Find x, y, and z.

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2. A photographer positions a camera on a tripod to take a picture of a grain silo. The lens of the camera is 4 feet 6 inches from the ground. To get the full height of the silo, the camera had to be positioned 18 feet from the base of the silo. How tall is the grain silo?

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3. Determine the value of cosB to the nearest hundredth.

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4. Complete the chart.

30 45 60

sin

cos

tan

5. Find the perimeter and area of the triangle. Round to the nearest tenth.

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6. Find YZ. Round to the nearest unit.

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7. Find m�D to the nearest degree.

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8. The length of a slide at a water park is 50 feet from the top of the slide to ground level. The top of the slide is 20 feet above the ground. What is the approximate measure of the angle formed by the top of the slide and the vertical support to the ground? Round to the nearest degree.

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Name ________________________________________ Date ___________________ Class __________________



Right Triangles and Trigonometry Chapter Test Form C continued

9.A plane is flying at a constant altitude of 30,000 feet and a constant speed of 750 miles per hour. A fisher on a lake spots the plane headed in his direction at an angle of elevation of 68. To the nearest minute, now much time will pass before the plane is directly over the fisher?

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10. A forest ranger in a 140-foot-tall observation tower sees a fire moving in a direct path toward a lake. The angle of depression to the fire is 38. The angle of depression to the lake is 88. To the nearest foot, how close is the fire to the lake?

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11. Find the perimeter of �ABC to the nearest tenth.

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12. The coordinates of the vertices of �JKL are J(�1, 4), K(2, 2), and L(�4,0). Find the measure of the smallest angle of the triangle. Round to the nearest degree.

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13. Identify another vector that is parallel to but NOT equal to the resultant vector of ��2, 7 � ��3, 3.

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14. Find the direction of ��6, 4. Round to the nearest degree.

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15. A skiff leaves a dock and heads toward a house across the river. The house is at a bearing of N 648 E from the dock. There is a 1 mile per hour current blowing due east. Determine the speed and direction the skiff would have to maintain so that the skiff’s actual speed is 4 miles per hour and it is moving directly toward the house. Round the speed to the nearest whole number and the direction to the nearest degree.

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Name ________________________________________ Date ___________________ Class __________________



Spatial Reasoning Chapter Test Form A

1. Classify the figure.

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2. Describe the three-dimensional figure that can be made from the net.

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3. Find the volume of the cube.

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4. Find the volume of the cylinder in terms of �.

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5. Find the volume of the pyramid.

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6. Find the volume of the cone in terms of �.

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Use the figure for Exercises 7 and 8.

7. Find the volume of the sphere in terms of �.

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8. Find the surface area of the sphere in terms of �.

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Name ________________________________________ Date ___________________ Class __________________



Spatial Reasoning Chapter Test Form B

1. How would you classify a three-dimensional figure that has a circular base and a vertex?

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2. Describe the three-dimensional figure that can be made from the net.

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3. Find the volume of the regular hexagonal prism. If necessary, round to the nearest tenth.

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4. Find the volume of a cylinder with a base area of 49� in2 and a height equal to twice the radius. If necessary, round to the nearest tenth.

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5. Find the volume of a rectangular pyramid with length 5 meters, width 3.4 meters, and height 8 meters. Round to the nearest tenth.

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6. Find the volume of the cone. Round to the nearest tenth.

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7. Determine the volume of a sphere with a great circle that has an area of 9� cm2.Give the answer in terms of �.

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8. Determine the surface area of a sphere if the diameter is 3 feet. Round to the nearest tenth.

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Name ________________________________________ Date ___________________ Class __________________



Spatial Reasoning Chapter Test Form C

1.Describe the faces and base(s) of a pentagonal prism.

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2. Describe the cross section formed by the intersection of a triangular pyramid and a plane parallel to the base of the pyramid.

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3. Three inches around both ends of the box will be cut and folded to form the top and bottom. Determine the volume of the box. If necessary, round to the nearest tenth.

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4. To the nearest cubic centimeter, determine the volume of packing peanuts needed to fill the box if the radius of the enclosed cylinder is 4 centimeters and the cylinder is centered in the box.

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5. A square pyramid has a slant height of 17 centimeters and a lateral area of 544 square centimeters. Determine the volume of the pyramid.

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6. There is a cone-shaped plug in the bottom of a cone. If the height of the plug is 5 inches and the height of the cone is 16 inches, determine the volume of the cone. If necessary, round to the nearest tenth.

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7. Determine the diameter of a sphere with a volume of 972� in3.

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8. Find the surface area in terms of � of a sphere with a volume of 288� cm3.

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Name ________________________________________ Date ___________________ Class __________________


238 Holt McDougal Geometry

End-of-Course Test Choose the best answer. 1. P is between J and K. The distance between J

and P is 7 more than3 times the distance between Pand K. If JK � 55, what is PK? A 12 C 24 B 16 D 29

2. QX bisects �PQR. What is the greatest possible whole-number measure of �PQX? F 458 H 908 G 898 J 1008

3. The ratio of the measures of two supplementary angles is 8 : 4. What is the measure of the smaller angle? A 12 � C 60 � B 40 � D 80 �

4. What is the distance between the points (4, -1) and (-2, 3)?

F 2 5 H 2 13

G 10 J 2 6

5. Which is next in the sequence? �1, 2, 7, 14, 23, . . . A 24 C 32 B 25 D 34

6. Which is the converse of the statement? If 6 � 3x 7, then 3x � �1.

F If 6 � 3x � 7, then 3x � �1. G If 3x �1, then 6 � 3x � 7. H If 6 � 3x �7, then 3x � 1. J If 3x � 1, then 6 � 3x �7.

7. Which conjecture is valid by the Law of Syllogism? Given: If it is June 12, then the local orchestra will play a concert. If the local orchestra is playing a concert in June, then the day must be Tuesday. A If it is June 12, then the day must

be Tuesday. B If the local orchestra is playing a concert,

then it must be June 12. C If the local orchestra is playing a concert,

then it must be a Tuesday in June.

D If it is a Tuesday in June, then the local orchestra is playing a concert.

8. In the figure, why is �QS QS ?

F All altitudes are congruent.

G Symmetric Property of Congruence

H Reflexive Property of Congruence J Transitive Property of Congruence

9. Which names a pair of corresponding angles?

A �1 and �6 C �2 and �7 B �3 and �8 D �3 and �7

10. What is the value of 12x � 20?

F 34 H 90 G 88 J 100

Name ________________________________________ Date ___________________ Class __________________

End-of-Course Test

11. What is the slope of the line that passes through the points (�1, 9) and (4, 6)?

A � 53

C 15

B � 35

D 5

12. Which is the equation of the line in the graph? F y � �2x � 3

G � � �3 32

y x

H y ��3x � 1

J � � �2 13

y x

13. Two of the three angle measures in a triangle are given. Which are angle measures of an acute triangle? A 11 � , 79 � C 11 � , 89 � B 11� , 59 � D 11 � , 29 �

14. Which polygon has line symmetry but not rotational symmetry? F rectangle H rhombus G square J kite

15. Which are the lengths of the sides of an obtuse triangle? A 8, 11, 15 C 11, 11, 15 B 9, 12, 15 D 10, 12, 15

16. What is the altitude of an equilateral triangle whose sides measure 42 centimeters?

F 21 H 21 3

G 42 J 42 3

17. What is the measure of one exterior angle of a regular polygon having 40 sides? A 4.5 � C 85.5 � B 9� D 171 �

The figure represents the wooden truss used to support the roof of a garage. Use the figure for Exercises 18 and 19.

18. What postulate or theorem can be used to prove �JKM � �LKM? F SSS H ASA G SAS J HL

19. Given that ML � 12 feet, how wide is the garage? A 12 ft C 25 ft B 24 ft D 26 ft

20. What is MP?

F 3 2 H 6

G 4 2 J 8

21. What is the value of x?

A 25 C 65 B 29 D 115

22. Which CANNOT be used to prove that a quadrilateral is a parallelogram? F One pair of opposite angles is congruent. G Both pairs of opposite sides are parallel. H Both pairs of opposite sides are congruent. J One pair of opposite sides is both parallel

and congruent.

Name ________________________________________ Date ___________________ Class __________________

End-of-Course Test

23. The figure represents a rectangular gate with diagonal braces. To the nearest tenth, what is the width, QT, of the gate?

A 3.9 ft C 7.0 ft B 4.9 ft D 7.6 ft

Refer to the figure for Exercises 24and 25.

24. Kim is making a kite with a wooden frame. The measures of the frame are shown. She will use cloth binding to cover the outer edges of the kite. To the nearest tenth, how many centimeters of binding will she need? F 58.1 cm H 116.2 cm G 82.1 cm J 164.3 cm

25. What is the area of the kite? A 200 cm2 C 1400 cm2

B 400 cm2 D 2800 cm2

26. To the nearest tenth, what is AP?

F 1.0 m H 2.5 m G 2.2 m J 4.7 m

27. �TUV undergoes the dilation: (x, y) � (2x, 2y).Then it is translated: (x, y) �(x � 10, y � 8). If vertex T was at (8, 6), what are its coordinates after these two transformations? A (16, 12) C (6, 4) B (–2, –2) D (–4, –4)

28. Starla is 5 feet 9 inches tall. To find the height of a tree, she measured her shadow and the tree’s shadow. Her shadow was 8 feet long when the tree’s shadow was 30 feet long. To the nearest foot, how tall is the tree? F 15 ft H 28 ft G 22 ft J 42 ft

29. MN with endpoints M(9, 3) andN(�1, 5) is dilated by a scale factor of 2.5. To the nearest tenth, what is the length of � �M N ? A 16.1 C 25.5 B 17.9 D 28.3

30. To the nearest thousandth, what is tan77�? F 0.225 H 0.974 G 0.231 J 4.331

31. The legs of a right triangle measure 11.4 meters and 15.1 meters. To the nearest tenth, which could be the measure of the smallest angle? A 31.1 � C 38.6� B 37.1 � D 52.9�

32. When the angle of elevation to the sun is 26� a flagpole casts a shadow that is 82 feet long. What is the height of the flagpole to the nearest foot? F 36 ft H 74 ft G 40 ft J 166 ft

33. The sides of a triangle measure 18 inches, 25 inches, and 36 inches. To the nearest degree, what is the measure of the largest angle? A 1138 C 1578 B 1478 D 1598

Name ________________________________________ Date ___________________ Class __________________


241 Holt McDougal Geometry

End-of-Course Test

34. �XYZ is reflected across the line y � x.If vertex Z is at (�15, 21), where is Z��after the reflection? F (15, 21) H (21, �15) G (15, �21) G (�21, 15)

35. MN with endpoints M(6, �10) and N(1, 0) is reflected over the y-axis, then translated right 5 units, and down 2 units. What is the coordinate of ''N ? A �(4, 2) C � �( 4, 2) B (4,2) D � �( 6, 2)

36. To the nearest tenth, what is the area of a regular octagon with a perimeter of 32 meters? F 77.3 m2 H 180.0 m2

G 154.5 m2 J 1024 m2

37. The area of a trapezoid is 128 square feet. If the height of the trapezoid is increased by a factor of 5, what is the area of the new trapezoid? A 133 ft2 C 640 ft2

B 138 ft2 D 3200 ft2

38. A rectangular scarf with the design shown is set out to dry. A fly lands on the scarf. What is the probability that it lands in the shaded region?

F 0.25 H 0.75 G 0.50 J 0.80

39. The air conditioner cycles on once every 28 minutes and stays on for 7 minutes. Find the probability that the air conditioner will be on when you walk in the door. A 0.2 C 4 B 0.25 D 5

40.What is the volume of a rectangular prism that is 4 inches wide, 9 inches long, and 3 inches high? F 36 cm3 H 324 cm3

G 108 cm3 J 432 cm3

41. To the nearest tenth, what is the volume of a cylinder with a diameter of 22 centimeters and a height of 13 centimeters? A 4941.7 cm3 C 6589.0 cm3

B 5321.9 cm3 D 19,766.9 cm3

42. What is the volume of a square pyramid with base area of 4 square meters and a height of 6 meters? F 6 m3 H 12 m3

G 8 m3 J 24 m3

43. To the nearest tenth, what is the area of a sector of a circle of radius of 9 meters if the central angle is 50�? A 1.3 m2 C 35.3 m2

B 5.1 m2 D 70.7 m2

Refer to the figure for Exercises 44 and 45. 44. � � �m 78 ,PN

� � �m 163.5 ,QN and� �m 72.MQ What is m�PRM?

F 47 � H 94 � G 57 � J 105 �

45. PR � 6, NR � 15, and QR � 14. To the nearest tenth, what is MR? A 5.6 C 6.4 B 6.0 D 7.0

46. The equation for a circle is (x � 4)2 � (y � 3)2 � 25. Which pair of coordinates locates its center? F (4, �3) H (16, �9) G (�4, 3) J (�16, 9)

Name ________________________________________ Date ___________________ Class __________________



Cumulative Test B Choose the best answer. 1. P, W, and K are collinear, and W is

between P and K. PW � 10x, WK �2x � 7, and PW � WK � 6x � 11.What is PK? A 25 C 90 B 65 D 115

2. ��RM bisects �VRQ. If m�MRQ � 828,what is m�VRM? F 41 � H 98 � G 82 � J 164 �

3. The measure of the complement of an angle is 59� . What is the measure of the supplement of the angle? A 31 � C 121 � B 39 � D 149 �

4. What is the midpoint of the segment whose endpoints are (17, 1) and (�9, 3)? F (8, 4) H (13, �1) G (4, 2) J (26, �2)

5. To the nearest tenth, what is the distance between the points (�12, 9) and (6, 10)? A 16.3 C 19.9 B 18.0 D 21.4

6. Which is the image of (�4, 7) rotated 180 � about the origin? F (4, �7) H (�4, 7) G (7, �4) J (�7, 4)

7. What is the next letter in the series? a b d g k p . . .

A q C v B u D z

8. If 7k � 12 and 6c � 7k, which is true by the Transitive Property of Equality? F c � 2 H 7k � 7k G 7k � 6c J 6c � 12

9. Which statement has a true converse? A If exactly two angles of a triangle are

acute, then the triangle is an acute triangle.

B If two angles of a triangle are congruent, then the sides opposite them are congruent.

C If the sum of two angles of a triangle is more than 90 � , then one of the two angles is obtuse.

D If no two angles of a triangle are congruent, then the triangle is not scalene.

10. Given: If two angles of a triangle are congruent, then the triangle is isosceles. If a triangle is isosceles, then two altitudes of the triangle are congruent. Which conjecture is valid by the Law of Syllogism? F If two angles of a triangle are

congruent, then the triangle is isosceles.

G If two altitudes of a triangle are congruent, then the triangle is isosceles.

H If two angles of a triangle are congruent, then two altitudes of the triangle are congruent.

J If two altitudes of a triangle are congruent, then the base angles of the triangle are congruent.

11. Which biconditional statement is false? A x � 1 if and only if x2 � 1. B Three points are collinear if and only

if one point is between the other two. C An angle is a straight angle if and

only if its sides are opposite rays. D A polygon is a triangle if and only if it

has exactly three sides.

Name ________________________________________ Date ___________________ Class __________________



Cumulative Test B continued 12. Which statement is true?

F r || s H q || s G q || r J p || q

13. What is the slope of the line that passes through (11, 7) and (3, 8)?

A �8 C 1412

B � 18

D 1514

14. What is the slope of a line parallel to a

line whose slope is � 52

?

F � 52

H 25

G � 25

J 52

15. Which is an equation of the line in the graph?

A � � �322

y x C � � �322

y x

B � �2 23

y x D 223

y x� �

16. The graph of which equation intersects the graph of y � �5x � 6 in one point? F y � 5 � 5(x � 1) G 5x � y � �3 H 10x � 2y � 3 J y � 5 � �5(x � 1)

17. Which segment lengths are the lengths of the sides of a scalene triangle? A 7, 7, 7 C 2, 3, 3 B 4, 5, 8 D 5, 5, 6

18. One angle of an obtuse triangle measures 168. Which could be another angle measure of the triangle? F 898 H 748 G 808 J 48

19. The sum of the measures of two angles of a triangle is 90� . Which type of triangle is it? A right C equilateral B obtuse D acute

20. A base angle of an isosceles triangle measures 32 � . What is the measure of the exterior angle at the vertex? F 16 � H 64 � G 32 � J 116 �

21. Which CANNOT be used to justify the statement �PQR � �TUV?

A SSS C AAS B SAS D ASA

22. A base angle of an isosceles triangle measures (3x � 9)� . The vertex angle measures 12x � . What is the measure of the vertex angle? F 12 � H 132 � G 108� J 156�


A 3 B 6

C 7.5 D 10.5

Name ________________________________________ Date ___________________ Class __________________



Cumulative Test B continued

24. In �RST, m�S � 49 � and m�T � 52 �Which list shows the side lengths from least to greatest? F ST, RT, RS H RT, RS, ST G ST, RS, RT J RT, ST, RS

25. Which inequality MUST be true?

A a � d C b c B c b D a d

26. Which segment measures could be the lengths of the sides of an acute triangle?

F 10, 15, 16 H 11, 5 6,18

G 10, 12, 2 61 J 11, 60, 61

27. The hypotenuse of a 308-608-908 triangle measures 10 3 inches. What is the measure of the longer leg? A 5 in. C 10 in.

B 5 3 in. D 15 in.

28. One leg of a 45-45-90 triangle measures 12 centimeters. What is the length of the hypotenuse?

F 4 3 cm H 12 2 cm

G 6 2 cm J 12 3 cm

29. What is the measure of one interior angle of a regular polygon that has 40 sides? A 9 � C 140 � B 40 � D 171 �

30. The diagonals of a rhombus are congruent. What is the best name for the figure? F parallelogram H rectangle G rhombus J square

31. In�WXYZ, find m�W.

A 878 C 918 B 898 D 938

32. One diagonal of a square divides the other into two segments measuring8 2 and 2y. What is the perimeter of the square?

F 16 2 2y� H 32 � 2 2y

G 32 � 2y J 64 33. One of the diagonals of a kite bisects two

of the angles into 508 and 448 angles. What is the measure of one of the other angles of the kite? A 48 C 868 B 88 D 1728

34. The figure PQRS is an isosceles trapezoid with � .PS QR

Which statement is NOT true? F �PTS � �QTR G �PQT � �RTS H �PSR � �QRS J �PQS � �QPR

35. In the figure, �JMK � �RMQ.What is JM?

A 9.6 C 14.4 B 11.2 D 21.6

Name ________________________________________ Date ___________________ Class __________________



Cumulative Test B continued

36. Raoul uses tongs to adjust logs in his fireplace. He opens the handles of the tongs 16 inches to move a log.

To the nearest inch, how wide is the log? F 6 in. H 10 in. G 7 in. J 36 in.

37. Drake wants to reduce an 8-inch by 10-inch photo so that the width is 5 inches. What will be the measure of the length? A 4 in. C 7 in.

B 164

in. D 16 in.

38. What is WY?

F 24 H 34 G 30 J 36

39. The shadow of a 6-foot man is 8 feet. At the same time, how long a shadow would a 90-foot monument cast?

A 265

in. C 67 ft 6 in.

B 1 ft 10 12

in. D 120 ft

40. �LMN was mapped to triangle �XYZ. If �LMN is similar to �XYZ what could the tranformation have been? F (x, y) � (4x, 5y) G (x, y) � (2x, 3y) H (x, y) � (5x, 4y) J (x, y) � (2x, 2y)

41. An altitude divides the hypotenuse of a right triangle into two segments measuring 3.6 and 6.4 centimeters. What is the length of the altitude? A 4.8 cm C 10 cm B 5 cm D 23.04 cm

42. One angle of a right triangle measures 27.48. The adjacent leg measures 7 yards. To the nearest tenth of a yard, what is the measure of the hypotenuse? F 3.6 yd H 7.9 yd G 6.2 yd J 15.2 yd

43. To the nearest tenth, the sides of a right triangle measure 56, 33, and 65. To the nearest degree, what is the measure of the smallest angle? A 30 � C 32 � B 31 � D 58 �

44. A helicopter pilot sights a landmark at an angle of depression of 22� The altitude of the helicopter is 1450 feet. To the nearest foot, what is the horizontal distance from the helicopter to the landmark? F 543 ft H 3589 ft G 586 ft J 3871 ft

45. Two sides of a triangular field measure 11.1 meters and 13 meters. The included angle measures 98 � . Find the measure of the third side to the nearest tenth of a meter. A 2.5 m C 18.2 m B 15.9 m D 48.4 m

46. A motorboat heads N 158 W to cross a river flowing 7.25 miles per hour due east. The boat travels at the speed necessary to head due north. To the nearest mile per hour, how fast is the motorboat traveling? F 2 mi/h H 27 mi/h G 8 mi/h J 28 mi/h

Name Date Class



Cumulative Test A Choose the best answer. 1. An angle measures 42 degrees more

than twice the measure of its complement. What is the measure of its complement? A 16 � C 46 � B 26 � D 106 �

2. The circumference of a circle is 134.7 square centimeters. Whatis the diameter of the circle to the nearest tenth? F 6.5 cm H 21.4 cm G 13.1 cm J 42.9 cm

3. M is the midpoint of .AB M has coordinates (�3, �8) and B has coordinates (�1, 6). What are the coordinates of point A? A (�5, �22) C (1, 20) B (�4, �1) D (5, 22)

4. What are the coordinates of the image of (�3, �7) after the translation (x, y) � (x � 9, y � 9)? F (�6, 16) H (12, �2) G (6, �16) J (�12, 2)

5. Which is the next number in the series? �1, 0, 3, 8, 15, 24, 35, . . . A 46 C 59 B 48 D 72

6. Which is the converse of the statement? If x 10, then y � �4.

F If x �10, then y � 4. G If y � 4, then x 10. H If x � 10, then y �4. J If y �4, then x � 10.

7. What is sin 49 � to the nearest tenth? A 0.7 C 1.2 B 0.8 D 1.3

8. Ray wants to prove the following theorem.

If two angles are complementary to two congruent angles, then the original two angles are congruent.

He draws this diagram.

Which is the best given information? F �QMR � �UMT G �QMR and �RMS are

complementary angles. �UMT and �TMS are complementary angles.

H ��

,SM QU and �UMT and �TMSare complementary angles.

J �QMR � �UMT, �SM QU


A 80 C 92 B 88 D 96

10. Which inequality shows all possible solutions for x? F x � 6 G x � 6

H 1 62

x

J 1 62

x

Name Date Class



Cumulative Test A continued

11. What is the slope of the line that passes through (7, 3) and (�2, 4)?

A �9 C 57

B � 19

D 75

12. Which line coincides with the graph of the line 2x � 6y � 12?

F y � 2x � 2 H � � �1 23

y x

G y � �3x � 2 J � �1 23

y x

13. What is the classification of �PQRaccording to its angles? A right B obtuse C acute D equiangular

14. What is m�K? F 158 G 258 H 458 J 558

15. Which can be used to prove �TUV � �VWT? A SAS B AAS C ASA D HL

16. What is m�R? F 458 G 52.58 H 638 J 758

17. If P is the incenter, what is PK? A 3.2 cm B 4.0 cm C 4.2 cm D 4.4 cm

18. What is x?

F 1 cm H 1.75 cm G 1.5 cm J 2 cm

19. Which could NOT be the length of the third side of a triangle if two of its sides measure 15 feet and 40 feet? A 20 ft C 40 ft B 30 ft D 50 ft

20. The lengths of the shortest and longest sides of an acute scalene triangle are 9 meters and 41 meters. Which could be the length of the third side? F 39 m H 41 m G 40.5 m J 42 m

21. One exterior angle of a regular polygon measures 248. What is the sum of the measures of the interior angles of the polygon? A 3608 C 23408 B 9908 D 37448

22. A city park is inthe shape of a parallelogram as shown. Two paths will be installed along the diagonals. What is the total length of the paths? F 6.3 yd H 15.1 yd G 12.6 yd J 17.6 yd

Name Date Class



Cumulative Test A continued 23. The figure is a rectangle.

What is x?

A 29 C 61 B 58 D 90

24. A water slide in the middle of a water park pool has opposite sides in the shape of a trapezoid. Half of the slide is below water level. What is the length of the base of the slide?

F 5.7 m H 7 m G 6 m J 7.8 m

25. Point Z in �XYZ has coordinates (5, –4).�XYZ was dilated by a scale factor of 0.8. Name the coordinates of the image of point V.

A (5.8, –3.2) C (4, –3.2) B (5.8, –4.8) D (–3.2, 4)

26. Two American flags of different dimensions are properly folded into two similar isosceles right triangles. The ratio of the length of the legs of the smaller triangle to that of the larger triangle is 4 : 5. If the length of the hypotenuse of the larger triangle is 2 feet, what is the length of the hypotenuse of the smaller triangle to the nearest tenth of a foot? F 0.1 ft H 1.6 ft G 0.6 ft J 2.5 ft

27. What is ST?

A 3.6 m C 9.8 m B 7.2 m D 10.8 m

28. A 5 foot 6 inch boy casts an 8-foot shadow at the same time a nearby building casts a 44-foot shadow. To the nearest foot, what is the height of the building? F 30 ft H 1000 ft G 64 ft J 1936 ft

29. What is the magnitude of the vector �7, �4 to the nearest tenth? A 2.4 C 8.1 B 5.7 D 9.0

30. The legs of a right triangle measure 14 and 25. To the nearest tenth of a degree, what is the measure of the angle opposite the shortest side? F 29.28 H 55.98 G 34.18 J 60.88

31. A forest ranger in a 100-foot observation tower sees a fire. The angle of depression to the fire is 48. To the nearest foot, what is the horizontal distance between the tower and the fire? A 100 ft C 1433 ft B 1430 ft D 1434 ft

32. If 2(x � 5) � 10, then what justifies the statement x � 5 � 5? F Distributive Property G Associative Property of Equality H Transitive Property of Equality J Division Property of Equality

33. To the nearest tenth, what is the area of the regular hexagon? A 120.0 cm2 C 519.6 cm2

B 240.0 cm2 D 1039.2 cm2

Name Date Class



Cumulative Test A continued

34. To the nearest tenth, what is the area of the shaded region? F 35.0 cm2

G 44.0 cm2

H 51.5 cm2

J 112.0 cm2

35. What is the area of a square with a diagonal of 16? A 256 C 128 B 16 D 64

36. A radio station reports news and weather every 20 minutes for 4 minutes. If the radio is turned on at a random time, what is the probability that the news and weather report is NOT on? F 0.2 H 0.6 G 0.4 J 0.8

37. The cross section of a three-dimensional figure is a circle. Which figure could it NOT be? A cone C prism B sphere D cylinder

38. The area of a parallelogram is 60 square inches. What is the area of the parallelogram if the

base is multiplied by 34

?

F 2333 in4

H 80 in2

G 45 in2 J 22106 in3

39. The volume of a cylinder is 80 cubic centimeters. If the diameter and height of

the cylinder are multiplied by 4 ,5

what is

the volume of the new cylinder? A 163.84 cm3 C 40.96 cm3

B 64.00 cm3 D 10.24 cm3

40. The radius and height of a cylinder are multiplied by 5. What is the effect on the volume?

F The volume is multiplied by 1 .5

G The volume is multiplied by 5. H The volume is multiplied by 25. J The volume is multiplied by 125.

41. To the nearest tenth, what is the area of a sector with a radius of 8 centimeters and a central angle of 45�? A 4.5 cm2 C 50.3 cm2

B 25.1 cm2 D 100.5 cm2

42. What is m�RST? F 27 � G 54 � H 76.5 � J 85.5�

43. What is the equation for the graph of the circle?

A (x � 3)2 � (y � 2)2 � 6 B (x � 3)2 � (y � 2)2 � 6 C (x � 3)2 � (y � 2)2 � 36 D (x � 3)2 � (y � 2)2 � 36

44. What is x? F 8 yd G 16 yd H 20 yd J 32 yd

geometry l1 2015 final review informational packet unit objectives · 2017-05-23 · 10. prove...

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