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Analytic GeometryEOCT Review
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Proofs• Which item can be given as a statement in a proof? • A. Given
B. Def. of congruent segmentsC. m<1 + m< 2= 180
D. Trans. Prop. of Equality
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Proofs• Identify the property that justifies the statement.
1.m = n, so n = m
2.KL = KL
3.p = q and q = -1, so p = -1
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Proofs• Algebraic Proof• Solve the equation below. Write a justification for each
step.• 1/5(a + 10) = -3
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Parallelograms• Properties of Parallelograms• - Opposite sides are parallel and congruent• - Opposite angles are congruent• - Consecutive angles are supplementary• - Diagonals bisect each other
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Parallelograms• WXYZ is a parallelogram.
• Find the measure of angle W.
• Find the value of x.
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Parallelograms• In parallelogram JKLM, what is the value of <K?
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Parallelograms• ABCD is a parallelogram. Find AB and BX.
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Parallelograms• In parallelogram DEFG, what is EG?
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Angles formed by Lines and Transversals• Corresponding Angles are congruent• Alternate Interior Angles are congruent• Alternate Exterior Angles are congruent• Same Side Interior Angles are supplementary
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Angles formed by Lines and Transversals• Find each angle measure.
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Angles formed by Lines and Transversals• Find x.
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Congruence• 5 Triangle Congruence Theorems
• Side-Side-Side• Side-Angle-Side• Angle-Angle-Side• Angle-Side-Angle• Hypotenuse Leg (right triangles only)
• Angle-Side-Side is NOT a theorem
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Congruence• If ΔKLM ≅ ΔRST, find the value of x.
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Congruence• What is the measure of angle U?
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Congruence• ΔJKL≅ ΔMNP. KL = 21x - 2, NP = 20x, LJ = 15x and PM
= 13x + 4. Find LJ.
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Congruence
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Similarity• 3 Triangle Similarity Theorems
• Side-Side-Side• Side-Angle-Side• Angle-Angle
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Similarity• What theorem proves the triangles are similar?
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Similarity• What theorem proves the triangles are similar?
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Similarity• What is the length of AC?
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Similarity• Find SP.
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Similarity
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Similarity
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Similarity• A drawing of a garden uses a scale of 1 in : 3 ft. Find the
length of the garden if the length on the drawing is 13 inches.
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Exterior Angles Theorem• Find measure of <RST.
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Midsegment Theorem• Find QR. What type of segment is QR?
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Midsegment Theorem
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Triangles • What is the length of the longest side of the triangle?
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Angle relationships in Triangles • What is the value of x if the acute angles of a right triangle
measure 8x° and 12x°?
• The angles of a triangle measure 4°, 86°, and 90°. Which classification of the triangle is correct?
• One angle of an equilateral triangle measures (4x - 20). What is the value of x?
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Special Right Triangles• There are 2 types of special right triangles:• 1. 45-45-90• In a 45-45-90 triangle, the legs have equal length and
the hypotenuse is the length of one of the legs multiplied by √2.
• 2. 30-60-90• In a 30-60-90 triangle, the hypotenuse is the length of
the shorter leg multiplied by 2, and the longer leg is the length of the shorter leg multiplied by √3.
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Special Right Triangles• 45-45-90• Find the value of x.
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Special Right Triangles• 30-60-90• Find the value of x.
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Trigonometry• SOHCAHTOA• Sin = opp/hyp• Cos = adj/hyp• Tan = opp/adj
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Trigonometry• 1. Find tan K.• 2. Find cos M.• 3. Find sin K.
• 4. To the nearest degree, what is the measure of <M?
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Trigonometry• A 24-foot ladder forms a 76° angle with the ground. The
top of the ladder rests against a building. To the nearest inch, how high up the building does the ladder reach?
• One acute angle of a right triangle measures 28°. To the nearest tenth, what is the length of the side opposite that angle if the hypotenuse measures 16 meters?
• A skateboard ramp makes a 22° angle with the ground. To the nearest foot, how high is the ramp?
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Trigonometry• 1. Find sin (1.54).
• 2. If sin A = 8/17, find the measure of angle A.
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Trigonometry• Use the figure below to find each of the following:• 1. m<A.• 2. length of AB• 3. m<B.
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Lines that Intersect Circles• Use the figure below to find each of the following:• Chord• Secant• Tangent• Diameter• Radius
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Lines that Intersect Circles• To the nearest tenth, what is the length of MN?
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Central and Inscribed Angles• A central angle is EQUAL to the measure of its
intercepted arc.
• An inscribed angle is HALF the measure of its intercepted arc.
• An angle inscribed in a semicircle is ALWAYS a right angle.
• If two inscribed angles intercept the same arc, the angles are congruent.
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Central and Inscribed Angles• Find the measure of arc JK. Then, find the measure of
arc JIL.
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Central and Inscribed Angles
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Central and Inscribed Angles
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Central and Inscribed Angles
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Central and Inscribed Angles
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Inscribed Quadrilaterals• Opposite angles in an inscribed quadrilateral are
supplementary.
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Arc Length• Find the measures of arcs MN and XY.• Formula is not on the sheet
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Sector Area• Find the areas of sectors BAC and QPR.• Formula is not on the sheet
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Spheres• Volume and Surface Area formulas are on the sheet
• Find the volume and surface area of the sphere.
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Spheres• Find the surface area of a sphere with a volume of 256Π
cm3
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Volume• All formulas are on the sheet• Find the volume of each figure below.
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Volume• Find the volume of the cylinder.
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Volume• Find the volume of each pyramid.
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Volume• Find the volume of the cone.
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Volume• Find the volume of the composite figures.