TEKS/STAAR - WCSscihighgeometry.weebly.com/uploads/9/3/4/9/9349798/six_weeks_2.pdfMATHEMATICS Geometry TEKS/STAAR Spiraled Practice 21-40 Brenda DeBorde [email protected] Juanita

MATHEMATICS Geometry

TEKS/STAAR Spiraled Practice 21-40

Brenda DeBorde [email protected] Juanita Thompson [email protected]

TEKSING TOWARD STAAR ©2012

TEKSING TOWARD STAAR

Algebra I Geometry

®

TEKS/STAAR SPIRALED PRACTICE 21 Geometry

TEKSING TOWARD STAAR © 2012 1. Cat 1/G.2B 2. Cat 2/G.5B 3. Cat 3/G.6C Page 1

1. Conjecture: A prism has its height tripled but the other dimensions remain unchanged. The

volume of the new prism should be three times the volume of the original prism. Which of the following is a correct statement about this conjecture?

A The conjecture is true because the original base area will triple and therefore the volume will be

three times the original volume.

B The conjecture is false because the original base area will triple and the height will triple therefore the volume will increase by a factor of 9.

C The conjecture is true because the volume formula of V = Bh becomes V = B(3h) = 3Bh which is three times the original volume.

D The conjecture is false because you cannot just change one dimension of a prism. 2. Start with a 1-unit by 2-unit non-shaded rectangle. In each iteration, the following steps occur for

the smallest non-shaded rectangles resulting from the previous iteration. Step 1: Divide the rectangle into 4 congruent rectangles by dividing the rectangle in half lengthwise

and widthwise. Step 2: Shade in the uppermost left rectangle. The first iteration is shown below. What fractional part of the 1-unit by 2-unit rectangle will be shaded after the second iteration?

F 12

G 34

H 58

J 716



3. The top, side, and front views of an object built with cubes are shown below. Which of the following is a correct representation of this object?

Top View Side View Front View

Front

Front

A B C D

Front

Front


TEKSING TOWARD STAAR © 2012 1. Cat 4/G.8B 2. Cat 5/G.11C 3. Cat 1/G.3A Page 1

1. »AB has a central angle of 45° . Circle P has a diameter of 16 centimeters.

What is the length of ¼ACB ? A 2π cm

B 12π cm

C 14π cm

D Not Here

2. In the diagram below, AD = 8 and DB =12.5. CD AB⊥ . Find the value of DC. F 10

G 12

H 20.5

J 15

3. What is the converse of the conditional statement given below? “If two angles are vertical angles, then the angles are congruent.” A “If two angles are not vertical angles, then the angles are not congruent.”

B “If two angles are congruent, then the angles are vertical angles.”

C “If two angles are not congruent, then the angles are not vertical angles.”

D “If two angles are vertical angles, then the angles are not congruent.”

D

A

B C

16 c

m

45° B

C

P

A


TEKSING TOWARD STAAR © 2012 1. Cat 2/G.4A 2. Cat 3/G.7B 3. Cat 4/G.8A Page 1

1. The diagram below shows a circle inscribed in a right triangle.

Which equation best represents the area, A, of the shaded region? A 48A x z π= −2 2

B 24A x z π= +2 2

C 24A x z π= −2 2

D 24 2A x z π= −2 2

2. In ∆ABC , side BC is represented by 3 20y x= − + . The midpoint of side AB is D and the midpoint of side AC is E. Which of the following could represent DE ?

F 1 13

y x= − + H 3 20y x= +

G 13

y x= J 3 2y x= − −

3. In the drawing below, AD = 4, AB = 3, DC = 12, A∠ and BDC∠ are right angles. What is the area of the polygon?

A 19 square units

B 56 square units

C 72 square units

D 36 square units

D

A

C

B

6x

8x

z


TEKSING TOWARD STAAR © 2012 1. Cat 5/G.11D 2. Cat 1/G.3B 3. Cat 2/G.5B Page 1

1. A rectangular prism has a volume of 32 cubic meters. The length, width and height are changed to

one-half their original size to create a new prism. What will be the volume of the new rectangular prism? A 16 cubic meters

B 8 cubic meters

C 4 cubic meters

D 256 cubic meters

2. One diagonal of a square has endpoints (0, 6) and (6, − 6).

Which of the following best describes the endpoints of the other diagonal? F ( − 3, − 3) and (8, 2) because the diagonals of a square must intersect each other

G ( − 2, − 3) and (8, 2) because the diagonals of a square must be perpendicular

H ( − 2, − 2) and (8, 2) because the diagonals of a square must share the same midpoint

J ( − 3, − 3) and (9, 3) because the diagonals of a square must be perpendicular bisectors of each other

x

y

-10 -9 -8 –7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10

10

9

8

7

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10



3. Determine the measure of B∠ .

A 150 ° B 145 ° C 135 ° D 175 °

(6w-15) °

(4w) °

(w) °

120 °

B

C

D

E

A


TEKSING TOWARD STAAR © 2012 1. Cat 3/G.7C 2. Cat 4/G.8B 3. Cat 5/G.11A Page 1

1. D is the midpoint of AC .

What is the length of AB ?

A 8 units

B 14 units

C 16 units

D 18 units

2. »AB has a central angle of 45° . The circle has a diameter of 20 centimeters.

What is the best estimate of the area of the sector bounded by »AB ?

F 100 cm 2

G 39 cm 2

H 25 cm 2

J 7.8 cm 2

3. Which transformation will generate similar non-congurent figures?

A translation

B reflection

C rotation

D dilation

A D C B

3x + 2 6x – 4 x

20 c

m

45° B

A


TEKSING TOWARD STAAR © 2012 1. Cat 1/G.3C 2. Cat 2/G.5B 3. Cat 3/G.7C Page 1

1. Which of the following could be used to disprove the statement?

All rectangles are squares.

2. Two cylinders are similar. The radius of the smaller cylinder is 3 inches and the radius of the larger

cylinder is 9 inches. If the height of the larger cylinder is 12 inches what will be the height of the smaller cylinder?

F 3 inches H 5 inches

G 4 inches J 6 inches

3. CD is shown below. M is the midpoint of CD .

Which of the following best represents the coordinates of M? A (0, − 2) C ( − 1, − 3)

B (0.5, − 2) D (2, − 2)

x -5 -4 -3 -2 -1 1 2 3 4 5

5

4

3

2

1

-1

-2

-3

-4

-5

y

C

D

6 units

4 units

4 units

4 units

4 units

4 units

3 units

3 units

A B

C D


TEKSING TOWARD STAAR © 2012 1. Cat 4/G.8D 2. Cat 5/G.11B 3. Cat 1/G.3D Page 1

1. A pyramid has a square base with a side length of 8 units. The slant height of the pyramid is 12

units. Which of the following expressions could be used to calculate the total surface area of the pyramid?

A 8 2 + 8 × 12 B 8 2 + 4(8 × 12)

C 8 2 + 4(8 12)2×

D 8 2 × 8 × 12 2. ABC∆ and DEF∆ are similar triangles.

If the side lengths of DEF∆ are 60% of the side lengths of ABC∆ , what is the length of BC ? F 12

G 10

H 4.3

J 13.2

8 u

12 u

15 ?

20 A B

C

D E

F

7.2


TEKSING TOWARD STAAR © 2012 1. Cat 4/G.8D 2. Cat 5/G.11B 3. Cat 1/G.3D Page 2

3. The table below shows the relationship between the measures of 1, A∠ ∠ and .B∠

Which conjecture best represents the information in the table?

A An exterior angle of a triangle will always have an odd measure.

B The interior angles of a triangle will be acute angles.

C The interior angles of a triangle will always have different measures.

D The measure of an exterior angle of a triangle will equal the sum of the measures of the two interior angles that are not adjacent to it.

1 A

B

∠m A ∠m B 1∠m 40 65 105 70 70 140 45 60 105 20 120 140


TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5C 2. Cat 3/G.6B 3. Cat 4/G.8D Page 1

1. Lone Oak Street and Nadar Street are parallel. Sea Star Street and Center Street are parallel. What is the measure of ∠ KHL, the angle created by the intersection of Utility Line and Sea Star

Street? A 28 °

B 22 °

C 12 °

D 50 ° 2. Jonas created a solid figure by folding the following net on the dotted lines.

What solid figure did Jonas create? F A triangular prism

G A pentagonal pyramid

H A triangular pyramid

J A rectangular pyramid

Nadar

Center

Utility Line

Lone Oak

Sea Star Street

130°

28° H

K L


TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5C 2. Cat 3/G.6B 3. Cat 4/G.8D Page 2

3. A pyramid has a square base with side lengths of 6 units and a height of 10 units. Find the volume

of the pyramid.

A 360 cubic units

B 120 cubic units

C 46 cubic units

D 80 cubic units

6 6

10

6


TEKSING TOWARD STAAR © 2012 1. Cat 5/G.11C 2. Cat 1/G.3E 3. Cat 2/G.5A Page 1

1. Right triangle DEF has legs of 4 and 8 units. Which of the following right triangles is similar to

triangle DEF?

12

9 5

16

8 5 8

24 8

12 3

A

B

C

D


TEKSING TOWARD STAAR © 2012 1. Cat 5/G.11C 2. Cat 1/G.3E 3. Cat 2/G.5A Page 2

2. A midpoint divides a segment into two congruent segments. In the sketch below, C is the midpoint

of AB .

Which statement can be justified with deductive reasoning?

F If AC = 4, then CB = 8.

G If AB = 10, then AC = 10.

H AC = CB

J If AC = x and CB = 7, then AB = 7x.

3. In the table below, 1∠ and 2∠ are same side exterior angles of parallel lines intersected by a

transversal.

If 1∠ has measure (a + b)° , what expression could be used to represent the measure of 2∠ ?

A (a + b)

B (a + b) − 180

C 180 − a + b

D 180 − (a + b)

A B C

Same Side Exterior Angles Measure of 1∠ Measure of 2∠

40 ° 140 ° 25.5° 154.5° 90 ° 90 °

(a + b) ° ?


TEKSING TOWARD STAAR © 2012 1. Cat 3/G.6C 2. Cat 4/G.9A 3. Cat 5/G.11D Page 1

1. The top, side, and front views of an object built with cubes are shown below.

How many cubes are needed to build the object?

A 7 C 13

B 6 D 15

2. In the sketch below, coplanar segments AB and CD are parallel segments. Angle 1 is a right angle.

Which of the following conjectures can be justified?

F AB and CD are congruent. H CD will be perpendicular to ←→

MN .

G ←→

MN will bisect AB . J AB will be perpendicular to CD .

3. An isosceles triangle has a base of c units and legs of d units. A new triangle is created by

increasing the legs by 3 units and decreasing the base by 2 units. How will the perimeter be affected by these changes?

A The new perimeter will be 6 units more than the original perimeter.

B The new perimeter will be 8 units more than the original perimeter.

C The new perimeter will be 1 unit more than the original perimeter.

D The new perimeter will be 4 units more than the original perimeter.

Top View Side View Front View

M N

A

B

C

D

1


TEKSING TOWARD STAAR © 2012 1. Cat 1/G.1C 2. Cat 3/G.7C 3. Cat 2/G.5B Page 1

1. 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− + − . What

is the taxicab distance between (2, 5− ) and (4, 10)?

A − 7

B 7

C 17

D 3

2. Vertices A and B of rectangle ABCD have coordinates ( − 9, 6) and (3, 2). What is the slope of AB ?

F 13

G 13

−

H 3

J 3−

3. Three equilateral triangles are drawn below. The side length, height and area of each are given.

If an equilateral triangle has area 36 3 , what would be the side length of the triangle?

A 12

B 6 3

C 18

D Not here

16 8 3

Area: 64 3

10 5 3

Area: 25 3

6 3 3

Area: 9 3


TEKSING TOWARD STAAR © 2012 1. Cat 4/G.8D 2. Cat 5/G.11D 3. Cat 1/G.2A Page 1

1. A cylindrical can hold three tennis balls. The height of the stacked balls is 9 inches.

About what percent of the volume of the can is occupied by the tennis balls?

A 67%

B 45%

C 33%

D 75%

2. The radius of one spherical ball is 15 centimeters. Another ball has a radius that is 5 centimeters

longer. About how much greater is the surface area of the larger ball than the smaller ball?

F 2,827 2cm

G 314 2cm

H 5,026 2cm

J 2,199 2cm


TEKSING TOWARD STAAR © 2012 1. Cat 4/G.8D 2. Cat 5/G.11D 3. Cat 1/G.2A Page 2

3. Marshall constructed a line parallel to a given line, m, using congruent corresponding angles. Which

of the following could represent his finished construction?

A B

m

m

m

C D

m


TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5D 2. Cat 3/G.7B 3. Cat 4/G.8A Page 1

1. Identify which of the following are Pythagorean triples? A a = 1, b = 1, c = 2

B a = 1, b = 3, c = 10

C a = 5, b = 10, c = 15

D a = 6, b = 8, c = 10 2. FG is graphed on the grid below. Which of the following equations best represents the perpendicular bisector of FG ?

F 2 17x y− =

G 2 7x y− = −

H 2 10y x= +

J 1722

y x= +

3. A circular dining table has a radius of 2 feet 9 inches. Which of the following best represent the

area of the top of the table? A 23.8 square feet

B 9.5 square feet

C 7.6 square feet

D 8.6 square feet

x

y

-10 -9 -8 –7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10

10

9

8

7

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

G

F



1. If the length and width 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. 2. Conjecture: Translations will create congruent figures.

To show this statement is true, Mary plotted a line segment and assigned the vertices variable ordered pairs. She used the origin as one endpoint. She assigned the other endpoint the coordinates (c, d). She let the translation be x units right and y units down. She wants to compare the length of the translated segment with the length of the original segment which is

2 2c d + . Which of the following shows the correct calculation for the length of the translated segment? F ( ) ( ) ( )c x d y x y c d − + + − + = +2 2 2 2 2 2

G 2 2( ( )) ( ( ) ( ) c c x d d y x y c d − − + − + − + = +2 2 2 2

H 2 2( ( )) ( ( )) ( ) ( ) x c x y d y c d c d − − + − − + = − + − = +2 2 2 2

J ( ( )) ( ( )) ( ) ( )x c x y d y c d c d − + + − − − = − + − = +2 2 2 2 2 2

3. The table below shows the relationship between the height and the volume of similar rectangular

prisms.

Which statement can be supported by the information in the table?

A To determine the volume of the similar prism with height 10, multiply 24 by 15

.

B To determine the volume of the similar prism with height 10, multiply 24 by 5.

C To determine the volume of the similar prism with height 10, multiply 24 by 53 .

D To determine the volume of the similar prism with height 10, multiply 24 by 25 .

Similar Rectangular Prisms Height

(centimeters) Volume

(cubic centimeters) 2 24 4 192 6 648 10 ?


TEKSING TOWARD STAAR © 2012 1. Cat 3/G.7B 2. Cat 4/G.8D 3. Cat 5/G.11C Page 1

1. Triangle ABC is shown below.

D is the midpoint of AC and E is the midpoint of AB . Which equation best describes DE ?

A 2 6 15x y− = C 2 6 15x y+ =

B 6 2 5x y− = D 3 12x y− = −

2. A sphere has a great circle with a radius of 2 feet. What is the approximate volume of the sphere?

F 113.1 cubic feet H 50.3 cubic feet

G 33.5 cubic feet J 12.6 cubic feet

3. In the diagram below, AD = 8, DB = 12.5 and CD AB⊥ . Find the value of DC.

A 10 C 20.5

B 12 D 15

x

y

-10 -9 -8 –7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10

10

9

8

7

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

A

C

B

2 feet

D

A

B C


TEKSING TOWARD STAAR © 2012 1. Cat 1/G.3A 2. Cat 2/G.5B 3. Cat 3/G.7B Page 1

1. What is the converse of the following conditional statement?

“If a number is an even number, it is divisible by 2.”

A “If a number is not an even number, it is not divisible by 2.”

B “If a number is odd, then it is not divisible by 2.”

C “If a number is divisible by 2, then it is an even number.”

D “If a number is not divisible by 2, then it is not an even number.” 2. Jennifer observed a pattern for the angles of triangles. She noticed they always had a sum of 180 ° .

She determined the value of the three angles in the triangle above to be −

F o o o50 , 30 , 90

G o o o20 , 30 , 130

H o o o50 , 40 , 90

J o o o45 , 45 , 90 3. Rectangle ABCD has vertex A with coordinates (5, 8) and vertex B with coordinates (3, 0). Which

of the following could represent the line containing vertices C and D of the rectangle?

A 4 2x y+ =

B 4 3 12x y− =

C 4 8x y− =

D 4 4x y− =

C

A B

130 °


TEKSING TOWARD STAAR © 2012 1. Cat 4/G.8A 2. Cat 5/G.11A 3. Cat 1/G.3B Page 1

1. Which of the following polygons will have an area of 24 3 square units? A An equilateral triangle with a side length of 8 units

B A square with an apothem of 2 3 units

C A regular hexagon with a side length of 4 units

D A regular pentagon with a perimeter of 20 3 units 2. Which statement best describes why trapezoid ABCD is similar to trapezoid GHIJ? F The ratio of the length of AB to the length of GH equals the ratio of the length of CD to the

length of GJ . G Both trapezoids have corresponding right angles A and H. H Trapezoid GHIJ is a result of a translation of trapezoid ABCD. J Trapezoid GHIJ is a result of a dilation of trapezoid ABCD.

x

y

-10 -9 -8 –7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10

10

9

8

7

6

5

4

3

2

1

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

A

D C

B

G

I J

H


TEKSING TOWARD STAAR © 2012 1. Cat 4/G.8A 2. Cat 5/G.11A 3. Cat 1/G.3B Page 2

3. Point C is on Circle A and point B is in the interior of the circle. Which of the following statements is

true?

A AB AC>

B AB AC<

C AB AC=

D 2AC AB=

A

B

C


TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5D 2. Cat 3/G.6A 3. Cat 4/G.8D Page 1

1. RST∆ is shown below.

If RT = 18 inches, what is the area of RST∆ ?

A 18 2 in. 2

B 36 2 in. 2

C 162 in. 2

D 81 in. 2

2. The intersection of a sphere and a plane is a circle with a radius of 6 centimeters. If the sphere has

a radius of 20 centimeters, about how far is the plane from the center of the sphere? F 14 cm

G 19 cm

H 6 cm

J 12 cm

R

S

T


TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5D 2. Cat 3/G.6A 3. Cat 4/G.8D Page 2

3. Use the ruler on your chart to measure the dimensions of the net of the rectangular prism to the

nearest centimeter.

Which of the following best describes the surface area of the prism?

A 48 square centimeters

B 46 square centimeters

C 92 square centimeters

D 102 square centimeters



1. Given right triangle FDG and EH FG⊥

If FE = 7, DG = 10 and EH = 4, what is the length of FG ?

A 20.5

B 17.5

C 28

D 10.5

2. The following table shows the relationship between the number of sides of a convex polygon and the

total number of distinct diagonals that can be drawn for the polygon.

Number of sides Number of distinct diagonals 3 0 4 2 5 5 7 14 14 ?

How many distinct diagonals will a convex polygon with 14 sides have? F 28

G 77

H 56

J 154

F E D

G

H

7

4 10



3. Marisol made the statement that an acute isosceles triangle must contain an obtuse angle. Her

partner pair, Jodie, said he did not agree with her. Which of the following triangles could he use to show Marisol she had made an incorrect statement?

A B

35° 45°

105°

30°

C D


TEKSING TOWARD STAAR © 2012 1. Cat 3/G.7A 2. Cat 4/G.8E 3. Cat 5/G.11C Page 1

1. Lines KN and JL intersect at M as shown below. Name a ray with endpoint K.

A MN→

B MK→

C NK→

D KN→

2. A rectangle board is divided into four rectangular parts as shown below.

If two points are randomly chosen from the interior of the rectangle, what is the probability the first point will be in area A and the second will be in area C?

F 1

40

G 12

H 598

J 532

M K L

J N

A

B

C

D

8 in. 8 in.

2 in.

5 in.

5 in.

2 in.


TEKSING TOWARD STAAR © 2012 1. Cat 3/G.7A 2. Cat 4/G.8E 3. Cat 5/G.11C Page 2

3. ABC∆ is a right triangle with altitude to the hypotenuse, CD , as shown below. Which of the following statements is correct based on similar triangles ADC and ACB?

A AB ADBC DC

=

B AD ACAC AB

=

C AC ADAB DC

=

D AB ADAC BC

=

A

D

B C

Documents

TEKS/STAAR - WCSscihighgeometry.weebly.com/uploads/9/3/4/9/9349798/six_weeks_2.pdfMATHEMATICS Geometry TEKS/STAAR Spiraled Practice 21-40 Brenda DeBorde [email protected] Juanita