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MATHEMATICS Geometry
TEKS/STAAR Spiraled Practice 1-20
Brenda DeBorde [email protected] Juanita Thompson [email protected]
TEKSING TOWARD STAAR ©2012
TEKSING TOWARD STAAR
Algebra I Geometry
®
TEKS/STAAR SPIRALED PRACTICE 1 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 1/G.1B 2. Cat 2/G.5B 3. Cat 3/G.6B Page 1
1. Caleb made a list of careers that he believes geometry is an important part of. His list included: a. architecture b. astronomy c. building construction d. graphic design e. navigation Which of the following statements is correct?
A Caleb’s list is complete.
B Caleb’s list is correct but incomplete.
C Caleb’s list is incorrect.
D Caleb’s list is incorrect and incomplete.
2. ABC∆ is similar to GHJ∆ .
What is the ratio of BC to HJ? F 3:4
G 4:3
H 2:1
J 1:2
A
B
C G
H
J
8 4 6
TEKS/STAAR SPIRALED PRACTICE 1 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 1/G.1B 2. Cat 2/G.5B 3. Cat 3/G.6B Page 2
3. Which of the following could be the net of a rectangular prism?
A B
C D
TEKS/STAAR SPIRALED PRACTICE 2 Geometry
TEKSING TOWARD STAAR 2012 1. Cat 4/G.8D 2. Cat 5/G.11B 3. Cat 1/G.3B Page 1
1. A paperweight in the shape of a cylinder has a circumference of 8π centimeters. Its height is 12
centimeters. What is the total surface area of the paperweight?
A 96π square centimeters
B 102π square centimeters
C 132π square centimeters
D 128π square centimeters
2. Triangle ABC is similar to triangle DFE. If AB = 12 units, DF = 8 units, and BC = 9 units, what is
the value of EF? F 10 units
G 6 units
H 7.5 units
J 5 units
3. Which of the following statements is not true for all rectangles?
A The sum of the four angles will be 360 degrees.
B Opposite sides will be parallel and congruent.
C When a diagonal is drawn, the angles will be bisected.
D Adjacent sides will be perpendicular.
A
B C E
D
F
Circumference : 8π cm
Height: 12 cm
TEKS/STAAR SPIRALED PRACTICE 3 Geometry
TEKSING TOWARD STAAR 2012 1. Cat 2/G.4A 2. Cat 3/G.7A 3. Cat 4/G.8A Page 1
1. Which expression represents the perimeter of the triangle below? A 5 3x + C 26 9x x+
B 7 6x + D +7 3x
2. Look at the sketch below. Which of the following points are collinear?
F A, B and D H A, C and E
G B, D and E J B, D and F
3. A circle has a circumference of 16π inches. Which of the following represents the area of the circle? A 64π square inches
B 16π square inches
C 64 square inches
D 8π square inches
3x
2 3x +
A B C
D
E
F
C =16π in.
TEKS/STAAR SPIRALED PRACTICE 4 Geometry
TEKSING TOWARD STAAR 2012 1. Cat 5/G.11A 2. Cat 1/G.1C 3. Cat 2/G.5D Page 1
1. A triangle with vertices ( − 3, 6), (5, 6) and (1, − 2) is shown below.
Which triangle below is similar to the figure above?
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TEKS/STAAR SPIRALED PRACTICE 4 Geometry
TEKSING TOWARD STAAR 2012 1. Cat 5/G.11A 2. Cat 1/G.1C 3. Cat 2/G.5D Page 1
2. In a non-Euclidean geometry called taxicab geometry we are looking at a geometry that lies on a square grid. The only paths you can travel are horizontal and vertical paths like the streets on a grid as shown below.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Which statement correctly compares the distance between points A and B using taxicab geometry
and Euclidean geometry? F The taxicab distance is 2 units less than the Euclidean distance.
G The taxicab distance is 2 units more than the Euclidean distance.
H The taxicab distance is 1 unit less than the Euclidean distance.
J The taxicab distance is 1 unit more than the Euclidean distance.
3. The numbers 10, 24 and 26 form a Pythagorean triple. Which of the following also form a
Pythagorean triple?
A 15, 36, 39
B 30, 70, 78
C 40, 96, 102
D 5, 12, 14
A
B
TEKS/STAAR SPIRALED PRACTICE 5 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 3/G.7C 2. Cat 4/G.8D 3. Cat 5/G.11D Page 1
1. Parallelogram ABCD has vertices A ( − 6, − 2), B ( − 2, − 6), C (6, − 6) and D (2, − 2). What is the
slope of diagonal AC of the parallelogram ABCD?
A 13
B 13
−
C 3
D − 3 2. The height of a cone measures 14 centimeters and the radius of the cone measures 5 centimeters. Which of the following best represents the volume of the cone?
F 79 cm3
G 366 cm3
H 467 cm3
J 1,099 cm3
3. Mrs. Jones has a rectangular flower bed that is 65 inches long and 36 inches wide. She increases
the length by 9 inches and the width by 5 inches to create a new flower bed. Which of the following best describes the relationship of the perimeter of the new flower bed and the old flower bed?
A The new flower bed has a perimeter that is 14 inches more than the perimeter of the old flower bed.
B The new flower bed has a perimeter that is 45 inches more than the perimeter of the old flower bed.
C The new flower bed has a perimeter that is 28 inches more than the perimeter of the old flower bed.
D The old flower bed has a perimeter that is 28 inches more than the perimeter of the new flower bed.
14 cm
5 cm
TEKS/STAAR SPIRALED PRACTICE 6 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 1/G.2A 2. Cat 2/G.5A 3. Cat 3/G.6C Page 1
1. The construction of a perpendicular at point P on line r is shown below. Which of the following conjectures will not be true? A P is the midpoint of ST
B Q is equidistant from T and S.
C Points Q, T, and S will form an isosceles triangle.
D QSP∠ will be a right angle.
2. The table below shows the length of a diagonal of a square and the area of the square. From the pattern above, which of the following would represent the area of a square with a diagonal length of n? F 2n
G n ÷ 2
H 2 2n ÷
J 2n - 2
P r
Q
T S
Squares Length of diagonal Area
1 0.5 2 2 3 4.5 4 8 n
TEKS/STAAR SPIRALED PRACTICE 6 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 1/G.2A 2. Cat 2/G.5A 3. Cat 3/G.6C Page 2
3. Which three-dimensional figure has the front, side and top views shown below?
Front Side Top
A B
Front
Front
Front
Front
C D
TEKS/STAAR SPIRALED PRACTICE 7 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 4/G.8E 2. Cat 5/G.11C 3. Cat 1/G.2B Page 1
1. A spinner with a 10 centimeter radius has 4 sectors. The green sector has a central angle of 150° .
The red sector has a central angle of 80° . The blue sector has a central angle of 60° . The brown sector has a central angle of 70° .
What is the probability that the spinner will land on green or blue?
A 718
C 512
B 712
D 1118
2. A right triangle has sides of 3, 4, and 5. Which of the following could not be the sides of a right triangle that would be similar to the original triangle?
F 10, 24, 26 H 15, 20, 25
G 12, 16, 20 J 7.5, 10, 12.5
3. Look at the Venn diagram for triangles below. Which conjecture is not true? A A triangle can be a scalene right triangle.
B An isosceles triangle can be a right triangle.
C All equilateral triangles are isosceles.
D A right triangle can be equilateral.
TRIANGLES
Equilateral
Right
Isosceles Scalene
Green
Blue
Red
Brown
TEKS/STAAR SPIRALED PRACTICE 8 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5C 2. Cat 3/G.7B 3. Cat 4/G.8F Page 1
1. The class was given the following figure. The students were asked to create three new drawings of the figure showing in the figure through a progression of transformations in the order of : translation, rotation, reflection. Four students' drawings are shown below. Which student correctly drew the movements in order?
A B C D
TEKS/STAAR SPIRALED PRACTICE 8 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5C 2. Cat 3/G.7B 3. Cat 4/G.8F Page 2
2. The diagonals of a rhombus are perpendicular. The equation of a diagonal of a rhombus is 5 3 8x y+ = . Which of the following could be the equation of the other diagonal? F 3 5 6x y+ = −
G 3 5 5x y− =
H 5 3 6x y− =
J 5 3 3x y+ = 3. A carpenter has a piece of lumber that is 1.5 meters long. He needs a piece that is 4.5 feet long.
He needs to know if his piece is long enough. Which of the following best describes his situation? (1 inch is approximately 2.54 centimeters.)
A Yes, he has enough and he will have about 13 centimeters left.
B Yes, he has enough and he will have about 5 centimeters left.
C No, he does not have enough. He will need a piece that is about 13 centimeters longer.
D No, he does not have enough. He will need a piece that is about 5 centimeters longer.
TEKS/STAAR SPIRALED PRACTICE 9 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 5/G.11D 2. Cat 1/G.3A 3. Cat 2/G.5B Page 1
1. A triangle has an area of 36 square units. If the dimensions of the triangle are increased to 11
3
their original size, what will be the area of the new triangle?
A 48 square units
B 72 square units
C 64 square units
D 192 square units 2. What is the contrapositive of the following conditional statement? If a rectangle is a square, then it has congruent adjacent sides.
F A rectangle is a square if it has congruent adjacent sides.
G A rectangle is not a square if and only if it does not have congruent adjacent sides.
H If a rectangle is not a square, then it does not have congruent adjacent sides.
J If the adjacent sides of a rectangle are not congruent, then the rectangle is not a square.
3. The figures below represent similar rectangles.
Which of the following represents the dimensions of a rectangle that would not belong to this set of similar rectangles?
A 4 units by 8 units
B 3.5 units by 7 units
C 10 units by 20 units
D 1 unit by 3 units
5 units 2.5 units
10 units
5 units
15 units
7.5 units
TEKS/STAAR SPIRALED PRACTICE 10 Geometry
TEKSING TOWARD STAAR 2012 1. Cat 3/G.6A 2. Cat 4/G.9A 3. Cat 5/G.11A Page 1
1. A square pyramid is intersected by plane X parallel to the base of the pyramid as shown below.
If AG = 0.4AC, which of the following statements can be justified?
A The area of the base of the smaller pyramid will be 0.4 times the area of the larger pyramid. B The volume of the smaller pyramid will be 0.4 times the volume of the larger pyramid.
C The smaller pyramid will be similar to the larger pyramid with a scale factor of 0.4.
D AG ADAC AH
=
2. If l n⊥ , what is the value of x?
F 25
G 15
H 30
J 20
l
n (6 4 )y x− ° ( 3 )x y+ °
F
X
C
D
E
G H
I J
A
TEKS/STAAR SPIRALED PRACTICE 10 Geometry
TEKSING TOWARD STAAR 2012 1. Cat 3/G.6A 2. Cat 4/G.9A 3. Cat 5/G.11A Page 2
3. Triangle ABC is dilated to create triangle A′B′C′ as shown below on the grid below.
Which statement appears to be true? A The center of dilation used to create triangle A′B′C′ was ( − 7, 8).
B The two triangles are congruent.
C The scale factor used to create triangle A′B′C′ was 0.5.
D Triangle ABC was reduced in size to create triangle A′B′C′.
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TEKS/STAAR SPIRALED PRACTICE 11 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 1/G.3C 2. Cat 2/G.5C 3. Cat 3/G.6B Page 1
1. Larry was given the following statements. Linear pairs are supplementary. 2∠ and 3∠ are a linear pair.
Using the given statements, which of following conclusions would be a valid conclusion for Larry to make?
A 2∠ and 3∠ are congruent. C 2∠ is acute.
B 2∠ and 3∠ are not supplementary. D 2∠ and 3∠ are supplementary.
2. Jamie wants to use one figure to tessellate a plane for a project. Which of the following should she not choose for her project?
F Equilateral triangle
G Regular hexagon
H Square
J Regular pentagon
3. Which net represents the surface area of the pentagonal prism?
A B
C D
TEKS/STAAR SPIRALED PRACTICE 12 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 4/G.9B 2. Cat 5/G.11C 3. Cat 1/G.3D Page 1
1. If CD is a base and CF is a leg of isosceles trapezoid CDEF, then which statement must be true?
A CD and CF are perpendicular.
B CD and EF are parallel.
C CF and DE are parallel.
D DE and EF are parallel.
2. In the diagram below, CD is the altitude to the hypotenuse of right traingle ABC. Which pair of triangles listed below are similar triangles?
F and ADC BDC∆ ∆
G and ADC ABC∆ ∆
H and CDA BDC∆ ∆
J and ABC BDC∆ ∆
3. Which of the following is an example of inductive reasoning?
A All right triangles contain one right angle. Triangle ABC is a right triangle; therefore it will contain a right angle.
B Martin observed a number pattern of 0, 10, 21, 33 and decided the next two terms would be 46
and 60. C If a triangle is isosceles, it has two congruent sides. Triangle ABC is isosceles; therefore it has two congruent sides. D If Barbara attends study sessions, she does well on her tests. If she does well on her tests, her mother rewards her. Barbara attends study sessions; therefore, she does well on her tests and receives a reward from her mother.
D
A
B C
TEKS/STAAR SPIRALED PRACTICE 13 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5D 2. Cat 3/G.7B 3. Cat 4/G.9C Page 1
1. Rhombus ABCD is shown below. The measure of angle ABC is 45 ° . Segment AF represents the height of the rhombus. If AF is 10 meters, which of the following best represents the length of a side of the rhombus? A 10 meters
B 5 2 meters
C 10 2 meters
D 5 meters
2. One side of a rhombus is defined by the equation 3 4 2x y− = . Which of the following equations
could define the opposite side of the rhombus?
F 4 3 3x y− =
G 3 4 5x y− =
H 6 8 6x y+ =
J 4 3 5x y− = −
3. LK , EL , DK and ED are segments of circle P as shown below. These segments are called chords.
EML∆ is similar to KMD∆ . Which of the following statements is always true?
A ∠ LKD is congruent to ∠ KLE.
B LK is longer than ED .
C EM MD KM ML× = ×
D ED is longer than a diameter.
D
A
C
10 meters
F
B
P D
E K
L
M
TEKS/STAAR SPIRALED PRACTICE 14 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 5/G.11B 2. Cat 1/G.3E 3. Cat 2/G.4A Page 1
1. If a right triangle has sides of 5, 12 and 13 centimeters, which of the following could be the side
lengths of a triangle similar to it?
A 10, 24, 25
B 9, 24, 26
C 17.5, 42, 45.5
D 20, 48, 56
2. The angles of a triangle are 53, 75 and x degrees. The following statements are to be used to find x.
Which order should the steps be used to find x? F 1, 3, 4, 2 G 4, 1, 3, 2 H 2, 1, 3, 4 J 4, 3, 1, 2
3. A rectangle has a perimeter of 102 inches. The length of the rectangle is 3.25 times as long as the
width of the rectangle. Using w for the width and y for the length, which of the following pairs of equations could be used to find the dimensions of the rectangle?
A 51
3.25w yy w
+ =
=
B 102
3.25w yw y
+ =
=
C 51
3.25 w yw y
+ =
= ÷
D 2 2 102
3.25w y
w+ =
= +
y
1. 128 + x = 180 2. x = 52 3. 128 + x – 128 = 180 – 128 4. 53 + 75 + x = 180
TEKS/STAAR SPIRALED PRACTICE 15 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 3/G.7C 2. Cat 4/G.9D 3. Cat 5/G.11C Page 1
1. Two points A and B are equidistant from point C. However, they are not collinear points. Point A has coordinates ( − 5, 3) and point B has coordinates (1, 8). Point C has coordinates (x, y). Which of the following is an appropriate representation for relationship among A, B, and C?
A 2 2 2 2( 1) ( 8) ( 5) ( 3)x y x y− − − = + − − C 2 2 2 2( 1) ( 8) ( 5) ( 3)x y x y− + − = + + − B 2 2 2 2( 8) ( 1) ( 5) ( 5)x y x y− + − = − + + D ( 1) ( 8) ( 5) ( 3)x y x y− + − = + + −
2. A candy box shaped like a right rectangular prism is shown below.
Which of the following statement is not true about the prism?
F The prism has exactly 6 faces.
G The prism has exactly 8 vertices.
H The prism has exactly 10 edges.
J All the faces are rectangles.
3. In the figure below, segment QR is perpendicular to QP and RS and PQR QRS∆ ∆∼ .
What is the length of QP ?
A 10 feet C 15 feet
B 20 feet D 9 feet
Q
12 feet
P
R S 16 feet
TEKS/STAAR SPIRALED PRACTICE 16 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5A 2. Cat 1/G.1C 3. Cat 3/G.6A Page 1
1. The measures of an exterior angle for 4 regular polygons are shown below in the sketch. Which expression best represents the measure of an exterior angle of a regular polygon with n sides?
A 360n
B (n - 2)(180)
C 360n
D 180n
2. In taxicab geometry the distance between two points, ( 1 1,x y ) and ( 2 2,x y ), is 1 2 1 2x x y y− + − . In
Euclidean geometry the distance between two points, ( 1 1,x y ) and ( 2 2,x y ), is 2 1 2 12 2( ) ( )x x y y− + − .
For which of the following points would the taxicab distance and the Euclidean distance be the same?
F (1, 1) and (2, 2)
G (5, 0) and ( 6, 10)
H (4, 0) and ( − 4, 0)
J (6, 1) and (3, 2)
3. If a plane intersects a cylinder perpendicular to the bases and passes through the centers of the
bases, which of the following best describes the intersection?
A circle
B parallelogram
C rectangle
D semicircle
90° 72° 60° 120°
TEKS/STAAR SPIRALED PRACTICE 17 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 4/G.10A 2. Cat 5/G.11D 3. Cat 1/G.1B Page 1
1. Triangle ABC is shown below.
Triangle ABC is translated so that C (3, − 1) is mapped to C′ (1, − 4). Which ordered pair best represents A′?
A (7, 3)
B (4, 3)
C ( − 1, 1)
D ( − 1, − 1)
2. A rectangle has dimensions of 5 inches and 8 inches. If the dimensions are doubled, what will be the perimeter of the new rectangle?
F 26 inches
G 40 inches
H 13 inches
J 52 inches
3. Euclidean Geometry has three terms that are called undefined terms. Two of the terms are point
and plane. The third term is
A ray
B line segment
C line
D angle
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TEKS/STAAR SPIRALED PRACTICE 18 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5D 2. Cat 3/G.7C 3. Cat 4/G.10B Page 1
1. When the angle of elevation of the sun measures 45 ° , a tower casts a 30-meter shadow.
Which of the following is the best estimate of the height of the tower, x? A 30 m C 17.3 m
B 26 m D 45 m
2. Rectangle ABCD has diagonals that intersect at point E. Which of the following best describe point E?
F (3, 3) H (1.5, 1.5)
G (1.5, 3) J ( − 1.5, − 1.5)
3. If P is the midpoint of US and TR , which congruency statement can be verified with deductive
reasoning?
A PUT RSP∆ ≅ ∆ C PUT PSR∆ ≅ ∆
B PTU PSR∆ ≅ ∆ D UPT RSP∆ ≅ ∆
U T
P
R S
30 meters
45 °
x
30 m
A B
C D
E
( − 5, − 3)
(8, 6)
TEKS/STAAR SPIRALED PRACTICE 19 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 5/G.11D 2. Cat 1/G.2A 3. Cat 2/G.5D Page 1
1. The radius of the larger sphere shown below was multiplied by a factor of 14
to produce a smaller
sphere.
How does the surface area of the smaller sphere compare to the surface area of the larger sphere?
A The surface area of the smaller sphere is 14
as large.
B The surface area of the smaller sphere is 1π
as large.
C The surface area of the smaller sphere is 18
as large.
D The surface area of the smaller sphere is 116
as large.
2. The construction below shows ∠ACB with bisecting ray CD.
Which of the following statements is not valid based on the construction?
F m ACD∠ = 12
m ACB∠ H m ACB∠ = 2m DCB∠
G m ACD∠ = m DCB∠ J m DCB∠ = 2m BCA∠
3. Identify which of the following sets of numbers are Pythagorean triples.
A 2, 4, 6 C 5, 12, 13
B 0.3, 0.4, 0.5 D 1, 1, 2
A
B
C
D
Radius = 14
r Radius = r
TEKS/STAAR SPIRALED PRACTICE 20 Geometry
TEKSING TOWARD STAAR © 2012 1. Cat 3/G.7A 2. Cat 4/G.8C 3. Cat 5/G.11D Page 1
1. Which point plotted below best represents 15 ? A Point M
B Point N
C Point O
D Point P
2. A right triangle has a hypotenuse of 26.2 inches and a leg of 17.2 inches. Which of the following best represents the length of the other leg?
F 9.0 inches
G 19.8 inches
H 31.3 inches
J 17.9 inches
3. If the length and height only of a rectangular prism are doubled, what effect will this have on the
volume of the prism?
A The new volume will be twice the original volume.
B The new volume will be four times the original volume.
C The new volume will be eight times the original volume.
D The new volume will increase by 4 cubic units.
3 3.25 3.5 3.75 4
M N O P
l 2l
h 2h
w w