texas geometry staar diagnostic

STAARTM

State of Texas Assessments of

Academic Readiness

Geometry

Practice Exam

Page | 1

1 The figure below was formed by joining 2 segments of equal length at common endpoint Y.

If points X, Y, and Z are non-collinear, which of the following statements regarding XZ must always be true?

A XZ = XY

B XZ = 2(XY)

C XZ > 2(XY)

D XZ < 2(XY)

2 A geometry student concluded:

If two sides and a non-included angle of one triangle are congruent to two sides and a non-included angle of another triangle, then the two triangles are congruent.

Which diagram can be used as a counterexample to the student’s conclusion?

C

B D

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Z

Y

X

3 Which set of statements represents a valid deductive argument?

A All quadrilaterals have 4 angles.All parallelograms have 4 angles.All quadrilaterals are parallelograms.

B All parallelograms have diagonals that bisect each other.All parallelograms have opposite sides that are parallel.All polygons whose diagonals bisect each other have opposite sides that are parallel.

C All rectangles have 4 right angles.All squares have 4 right angles. All rectangles are squares.

D All parallelograms have 4 sides.All polygons with 4 sides are quadrilaterals. All parallelograms are quadrilaterals.

4 In each of the circles below, four angles are formed by the intersection of 2 secant lines. The measures of two intercepted arcs and one angle are shown for the first three circles.

Which expression can be used to represent m ABC in degrees?

A12

[(5x + 2) − (4x + 4)]

B12

[(5x + 2) + (4x + 4)]

C 2[(5x + 2) − (4x + 4)]

D 2[(5x + 2) + (4x + 4)]

Page | 3

68˚ 77˚ 86˚

25˚

32˚

39˚

82˚ 91˚ 100˚

(5x+ 2)˚

(4x + 4)˚

B

CA

5 Jake took pictures of Ana’s flag while she was practicing her routine for the football game, as shown below.

4

Which of the following best describes the movement of the flag from picture to picture?

A Reflection, rotation, translation

B Rotation, translation, translation

C Rotation, translation, dilation

D Reflection, translation, translation

6 When viewed from above, the base of a water fountain has the shape of a hexagon composed of a square and 2 congruent isosceles right triangles, as represented in the diagram below.

Top View

Base of F

ountain

Which of the following measurements best represents the perimeter of the water fountain’s base in feet?

A (20 + 20 2) ft C (40 + 20 2) ft

B (20 + 40 2) ft D (40 + 40 2) ft

Page | 4

10 ft.

40 ft.

7 A side view of the intersection of a plane and a square pyramid is modeled below.

Plane

Base of pyramid

Which of the following best represents the shape formed by this intersection?

C

B D

8 The three-dimensional figure shown is composed of 11 identical cubes.

Which of the following could not represent a top, front, or side view of the figure?

C

B D

Front

9 RG is graphed on the coordinate grid below.

Which of the following equations best represents the perpendicular bisector of RG?

A y=13x−2 C y=3 x−10

B y=−3x+8 D y=−13x+1

10 Half of an international basketball court is shown below. The shaded region is composed of an isosceles trapezoid and a semicircle. The diameter of the semicircle is 3.6 meters.

3.6 m

5.8 m

6.0 m

If 1 meter is approximately equal to 3.28 feet, which of the following is closest to the area of the shaded region in square feet?

A 32.9 ft.2 C 354 ft.2

R

G

y

x

B 409 ft.2 D 108 ft.2

11 In quadrilateral ABCD, AB CD, A ≅ B, and AB CD. Which of the following statements is areasonable conclusion?

A mA ≅ mC

B Quadrilateral ABCD is a rectangle.

C Quadrilateral ABCD is an isosceles trapezoid.

D AD BC

12 Triangles RST and VSU are shown below.

R ≅ V , and RT ≅ VU. Which additional condition is sufficient to prove that RS ≅ SV ?

A TS ≅ SU

B VS ⏊ RU

C RS ≅ SU

D VUS ≅ RST

U

V

S

T

R

13 A tree’s shadow is 4.8 m long on level ground, as shown in the diagram.

The angle of elevation from the tip of the shadow to the sun is 50°. Based on this information, which of the following is closest to the height of the tree?

A 3.6 m

B 5.7 m

C 3.1 m

D 7.5 m

14 A company packages their product in two sizes of cylinders. Each dimension of the larger cylinder is twice the size of the corresponding dimension of the smaller cylinder.

Based on this information, which of the following statements is true?

A The volume of the larger cylinder is 2 times the volume of the smaller cylinder.

B The volume of the larger cylinder is 4 times the volume of the smaller cylinder.

C The volume of the larger cylinder is 8 times the volume of the smaller cylinder.

D The volume of the larger cylinder is 6 times the volume of the smaller cylinder.

4.8 m

50˚

2d

2h

d

h

15 Points A (-2, 8) and B (5, 3) are vertices of square ABCD.

What is the slope of segment BC?

A 75

C −75

B −57

D 57

16 Use the proof to answer the question below.

Given: AB≅ BC; D is the midpoint of AC

Prove: △ABD ≅ △CBD

Statement Reason

1. AB ≅ BC; D is the midpoint of AC 1. Given

2. AD ≅ CD 2. Definition of Midpoint

3. BD ≅ BD 3. Reflexive Property

4. △ABD ≅ △CBD 4. ?

What reason can be used to prove that the triangles are congruent?

A AAS

B ASA

C SAS

D SSS

C

D

A

B

y

x

A

B

17 In the figure below, AC ≅ DF and A ≅ D.

Which additional information would be enough to prove that △ABC ≅ △DEF ?

A AB ≅ DE

B AB ≅ BC

C BC ≅ EF

D BC ≅ DE

18 Which of the following facts would be sufficient to prove that triangles ABC and DBE are similar?

A CE and BE are congruent. C AC and DE are parallel.

B ACE is a right angle. D A and B are congruent.

C

A B

F

ED

C E B

D

A

19 In the figure below, n is a whole number. What is the smallest possible value for n?

A 1 C 8

B 7 D 15

20 A circle is inscribed in a square, as shown below.

If a point is randomly chosen inside the square, what is the approximate chance that the point lies outside the circle?

A 21% C 73%

B 27% D 79%

21 In the diagram, GH IJ

15

nn

11 in.

If the mGLK = 55˚ and mEFJ = 120˚, what is mKEF?

A 55° C 65°

B 60° D 70°

22 A gardener wants to enclose a circular garden with a square fence, as shownbelow.

If the circumference of the circular garden is about 48 feet, which of the following is the approximate length of fencing needed?

A 31 ft. C 122 ft.

B 61 ft. D 244 ft.

23 Triangle ABC is similar to triangle DEF. The lengths of the sides of △ABC are 5, 8, and 11. What is the length of the shortest side of △DEF if its perimeter is 60?

KI J

F

E

LHG

A 10

B 12.5

C 20

D 27.5

24 A company makes sealed metal water tanks, as shown below.

To the nearest square meter, how much sheet metal does the company need to make one tank?

A 314 m2

B 471 m2

C 785 m2

D 942 m2

25 A sign is shaped like an equilateral triangle.

10 m

10 m

36 in.

If one side of the sign is 36 inches, what is the approximate area of the sign?

A 1,296 in.2 C 561 in.2

B 648 in.2 D 108 in.2

26 What is the surface area of the solid shown below?

A 72 cm2

B 144 cm2

C 156 cm2

D 184 cm2

27 The circle shown is divided into six equal sectors. The area of the circle

is 144π.

12 cm

5 cm

4 cm

What is the perimeter of the shaded sector?

A 12 + 3π C 24 + 24π

B 24 + 4π D 12 + 4π

28 City engineers plan to build Jordan Avenue according to the diagram below.

To the nearest foot, how long is the portion of the road between 2nd St. and 3rd St.?

A 375 ft. C 525 ft.

B 488 ft. D 867 ft.

29 △MNO is shown below.

Jordan Ave

650 ft.

375 ft.

x ft.

500 ft.Kyle St3rd St2nd St1st St

28 in.

25 in.12 in.

O

N

M

Which statement about this triangle is true?

A mO > mM

B mM > mN

C mM < mN

D mN < mO

30 Given the statements:

Linear pairs are supplementary.1 and 2 are supplementary.

Using either one or both of the statements, which conclusion is valid?

A 1 and 2 form a linear pair.

B Angles that are not supplementary are not linear pairs.

C 1 ≌ 2

D Supplementary angles are linear pairs.

31 Maia makes flower boxes to sell at a farmer’s market. One flower box is shown below.

36 in.

12 in.

8 in.

Maia wants to make another flower box that has a length of 24 inches instead of 36 inches. What will be the difference in volumes of the two flower boxes?

A 480 in.3

B 1,152 in.3

C 2,304 in.3

D 3,456 in.3

32 If the pattern shown below continues, how many dots will appear in the 7th figure?

A 31 dots

B 35 dots

C 55 dots

D 71 dots

33 Line m intersects line n to form a 90° angle. The equation of line m is y=7 x−4. If line n passes through (-7, -2), what is the equation of line n?

A y=7 x+7

B y=7 x+47

C y=−17x−3

D y=−17x−51

7

1151

34 Tim is designing his house. His outline of the front of the house and garage is shown below.

If he uses a scale of 1.5 in. = 14 ft., what would be the actual length of this side of the house and garage?

A 98 ft.

B 126 ft.

C 147 ft.

D 189 ft.

35 What is the mDAR in circle A?

10.5 in. 3 in.

34°B

R

D

A

A 17°

B 34°

C 56°

D 68°

36 A rectangular rug is 24 feet long and 10 feet wide. A rhombus design is formed inside the rug by joining the midpoints of each side of the rectangle. What is the length of each side of the rhombus?

A 13 ft.

B 26 ft.

C 169 ft.

D 240 ft.

37 Trapezoid TRAP is shown below.

NM

A (10, 3)R (5, 3)

P (15, 0)T (0, 0)

What is the length of midsegment MN?

A 10 C √234

B 252

D 100

38 The city’s zoning department has regulations to determine clear vehicle sight lines—called a Clear View Triangle—at all its intersections, as shown below.

If the mF = 90°, mG = 45°, and FG = 75 feet, what is EG?

A 150 ft. C75

√2 ft.

B 75√3 ft. D 75√2 ft.

39 The figure below is a tessellation of a quadrilateral.

What is the value of x?

tessellationquadrilateral

140°100°

70°

x°140°70°100°

A 20° C 50°

B 40° D 100°

40 What is the contrapositive of the statement below?

If a triangle is isosceles, then it has two congruent sides.

A If a triangle does not have two congruent sides, then it is not isosceles.

B If a triangle is isosceles, then it does not have two congruent sides.

C If a triangle has two congruent sides, then it is isosceles.

D If a triangle is not isosceles, then it does not have two congruent sides.

41 As shown in the diagram below, EF intersects planes P, Q, and R .

If EF is perpendicular to planes P and R , which statements must be true?

A Plane P is perpendicular to plane Q .

B Plane R is perpendicular to plane P.

FE

QP

R

C Plane P is parallel to plane Q .

D Plane R is parallel to plane P.

42 △ABC is a triangle in the coordinate plane. Points A (5, 6) and B (4, 5) are equidistant from

point C (x, y). What equation could be used to prove that △ABC is isosceles?

A √ (4+x )2+ (5+ y )2=√ (5+x )2+ (6+ y )2

B √ (4−x )2+(5− y )2=√ (5−x )2+ (6− y )2

C √ (4−x )2−(5− y )2=√ (5−x )2−(6− y )2

D √ (4+x )2−(5+ y )2=√ (5+x )2−(6+ y )2

43 What is the length of AB with endpoints A(-1,0) and B(4,-3)?

A √6

B √18

C √34

D √50

44 This figure shows a pattern of triangles and regular hexagons.

What is the value of x?

A 30°

B 60°

C 90°

D 120°

45 A fish tank in the shape of a rectangular prism has these dimensions:

• length = 20 inches

• width = 10 inches

• height = 12 inches

What is the volume of water in the tank when it is 45

full?

A 1,120 cu. in.

B 1,920 cu. in.

C 2,400 cu. in.

D 3,000 cu. in.

x°

46 The 12-foot-long bed of a dump truck loaded with debris must rise to an angle of 30° before the debris will spill out.

Approximately how high must the front of the bed rise for the debris to spill out?

A 1.7 ft.

B 18 ft.

C 10.4 ft.

D 6 ft.

12 ft.

30°

47 Which Pythagorean triple would be most helpful in finding the value of a?

A 3-4-5

B 5-12-13

C 8-15-17

D 7-24-25

48 Michelle is cutting pieces of wood to make shelves. Which must be true if Michelle’s shelves are rectangular?

A The diagonals are perpendicular.

B There are four congruent sides.

C The consecutive interior angles are not congruent.

D The diagonals are congruent.

49 Which triangle must be similar to the triangle shown below?

a

60

68

A C

B D

50 A rope is tied to the bottom of a hot air balloon as shown below. The rope makes an angle of 35° with the ground and is 75 ft. long.

How far is the bottom of the balloon from the ground to the nearest foot?

A 43 ft. C 61 ft.

B 53 ft. D 131 ft.

51 Max wants to wrap a box in the shape of a rectangular prism that is 2 ft. long, 1 ft. high, and 1.5 ft. deep.

How much wrapping paper is needed to cover the exact surface area of the box?

A 3 ft.2

B 4.5 ft.2

C 6.5 ft.2

D 13 ft.2

52 Which theorem can be used to show that the two triangles below are congruent?

A AAA

B ASA

C SAS

D SSS

Item Reporting Readiness or Content Student CorrectNumber Category Supporting Expectation Answer

1 1 Readiness G.2(B) D

2 1 Readiness G.3(C) D

1 ft.

1.5 ft.

2 ft.

7

9

9

7

3 1 Supporting G.3(E) D

4 2 Readiness G.5(A) B

5 2 Supporting G.5(C) A

6 2 Readiness G.5(D) D

7 3 Supporting G.6(A) D

8 3 Supporting G.6(C) C

9 3 Readiness G.7(B) A

10 4 Supporting G.8(F) C

11 4 Supporting G.9(B) C

12 4 Readiness G.10(B) B

13 5 Readiness G.11(C) B

14 5 Readiness G.11(D) C

15 5 Readiness G.11(D) A



18 5 Readiness G.11(C) C

19 1 Readiness G.2(B) C

20 4 Supporting G.8(E) A

21 4 Supporting G.9(A) C


23 5 Readiness G.11(D) B




27 4 Supporting G.8(B) B

28 5 Supporting G.11(B) B




32 1 Supporting G.3(D) C


34 4 Supporting G.8(F) B

35 4 Supporting G.9(C) D

Item Reporting Readiness or Content Student CorrectNumber Category Supporting Expectation Answer

36 2 Readiness G.5(D) A



39 2 Supporting G.5(C) C

40 1 Supporting G.3(A) A

41 3 Readiness G.6(A) D


43 3 Readiness G.7(C) C

44 2 Supporting G.5(B) A





49 5 Readiness G.11(C) D

50 5 Readiness G.11(C) A



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