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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


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


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


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.


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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y

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A

B

C

D


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


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


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


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


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


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


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.


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



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



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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y

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B

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A′

B′

C′


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


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


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


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


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


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°


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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y

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C


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)


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


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

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