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Final Exam Study Guide — Geometry (Grade 9)

Total questions: 144

Worksheet time: 1hrs 12mins

Name
Class
Date
1.

Complete each congruence statement by naming the corresponding angle or side. ΔPQR ≅ ΔLJK. ∠R ≅ ?

a)

∠J

b)

∠L

c)

KL

d)

∠K

e)

JK

2.

Complete each congruence statement by naming the corresponding angle or side. ΔFGH ≅ ΔFGJ. ∠H ≅ ?

a)

∠FGJ

b)

None of these

c)

∠G

d)

∠JFG

e)

JF

3.

Solve for x using the segment shown: LM = 3x + 3, MN = 11, and LN = 10x.

a)

2

b)

12

c)

1

d)

7

e)

0

4.

Solve for x using the segment shown: VU = x, UT = 2x − 4, and VT = 14.

a)

6

b)

3

c)

7

d)

5

e)

−6

5.

Find the midpoint of the line segment with the given endpoints: (−8, 6), (2, 0).

a)

(1 1/2, −8)

b)

(12, −6)

c)

(−3, 3)

d)

None of these

e)

(−1, 1)

6.

Find the midpoint of the line segment with the given endpoints: (−9, −10), (−2, −9).

a)

(5 1/2, −9 1/2)

b)

(−3 1/2, −1/2)

c)

(−9 1/2, −5 1/2)

d)

(−5, −4 1/2)

e)

(5, −8)

7.

Find the distance between the points (7, −6) and (3, 0).

a)

2√13

b)

5√2

c)

4

d)

2√34

e)

√10

8.

Find the distance between the points (7, 2) and (−7, −8).

a)

√6

b)

2√74

c)

2√2

d)

2√6

e)

6

9.

m∠GHD = 34° and m∠GHI = 174°. Find m∠DHI.

a)

140°

b)

128°

c)

162°

d)

None of these

e)

95°

10.

m∠JIH = 180° and m∠RIH = 160°. Find m∠JIR.

a)

20°

b)

27°

c)

28°

d)

22°

e)

24°

11.

Find the measure of angle b.

a)

21°

b)

57°

c)

147°

d)

33°

e)

159°

12.

Find the measure of angle b.

a)

None of these

b)

48°

c)

66°

d)

42°

e)

45°

13.

Find the value of x.

a)

13

b)

14

c)

None of these

d)

11

e)

15

14.

Find the value of x.

a)

35

b)

29

c)

34

d)

31

e)

32

15.

Find the interior angle sum for each polygon. Round your answer to the nearest tenth if necessary. The polygon shown is a hexagon.

a)

900°

b)

None of these

c)

1440°

d)

540°

e)

360°

16.

Find the interior angle sum for each polygon. Round your answer to the nearest tenth if necessary. The polygon shown is a pentagon.

a)

720°

b)

540°

c)

1440°

d)

None of these

e)

900°

17.

Find the measure of one interior angle in each regular polygon. Round your answer to the nearest tenth if necessary. The polygon shown has seven sides.

a)

120°

b)

128.6°

c)

None of these

d)

90°

e)

144°

18.

Find the measure of one interior angle in each regular polygon. Round your answer to the nearest tenth if necessary. The polygon shown is a pentagon.

a)

120°

b)

140°

c)

90°

d)

None of these

e)

108°

19.

Find the measure of one exterior angle in each regular polygon. Round your answer to the nearest tenth if necessary. The polygon shown is a hexagon.

a)

32.7°

b)

60°

c)

72°

d)

90°

e)

None of these

20.

Find the measure of one exterior angle in each regular polygon. Round your answer to the nearest tenth if necessary. The polygon shown is a square.

a)

60°

b)

45°

c)

51.4°

d)

40°

e)

None of these

21.

Find the slope of the line through each pair of points: (12, −6), (−6, 5).

a)

−3/2

b)

−11/18

c)

11/18

d)

None of these

e)

−18/11

22.

Find the slope of the line through each pair of points: (20, 8), (20, 3).

a)

0

b)

Undefined

c)

1/2

d)

−1/2

e)

−1/3

23.

Write the slope-intercept form of the equation of each line shown on the graph.

a)

y = −(4/5)x − 2

b)

y = −2x + 4/5

c)

y = (2/5)x − 2

d)

y = (4/5)x − 2

e)

y = (1/5)x − 2

24.

Write the slope-intercept form of the equation of each line shown on the graph.

a)

y = x + 5

b)

y = 5x + 1

c)

None of these

d)

y = 4x + 5

e)

y = −x + 5

25.

Write the slope-intercept form of the equation of the line described: through (−3, 1), parallel to x = 0.

a)

x = 3

b)

y = 3/2

c)

y = x − 3/2

d)

x = −3

e)

None of these

26.

Write the slope-intercept form of the equation of the line described: through (2, 5), parallel to y = x + 1.

a)

y = −2x + 3

b)

y = 3x − 2

c)

y = 2x + 3

d)

None of these

e)

y = −x + 3

27.

Write the slope-intercept form of the equation of the line described: through (−4, −5), perp. to y = −(4/7)x + 2.

a)

y = (7/4)x − 2

b)

y = −(7/4)x + 2

c)

y = −2x − 7/4

d)

None of these

e)

y = 2x − 7/4

28.

Write the slope-intercept form of the equation of the line described: through (−2, 0), perp. to y = (1/2)x − 3.

a)

y = 2x − 4

b)

y = −2x − 4

c)

y = −x − 4

d)

y = −4x + 2

e)

None of these

29.

Write the slope-intercept form of the equation of each line: 11x + 8y = −24.

a)

y = −3x − 1/4

b)

y = −(11/8)x − 3

c)

y = (1/4)x − 3

d)

y = x − 3

e)

y = −(1/4)x − 3

30.

Write the slope-intercept form of the equation of each line: 3x − 4y = 8.

a)

y = (3/4)x − 2

b)

y = −(3/4)x − 2

c)

y = −2x − 5/4

d)

y = (1/2)x − 5/4

e)

y = −(5/4)x − 2

31.

Find the measure of each angle indicated.

a)

None of these

b)

84°

c)

129°

d)

130°

e)

75°

32.

Find the measure of each angle indicated.

a)

44°

b)

53°

c)

94°

d)

141°

e)

102°

33.

Solve for x. Two parallel lines are cut by a transversal. One interior angle is labeled 105° and the corresponding interior angle on the other line is labeled 11x − 2.

a)

−5

b)

7

c)

None of these

d)

−4

e)

−7

34.

Solve for x. Two parallel lines are cut by a transversal. The angle on the upper line is labeled 17x − 6 and the interior angle on the lower line is labeled 7x − 6.

a)

3

b)

10

c)

None of these

d)

8

e)

−3

35.

State if the three numbers can be the measures of the sides of a triangle. 11, 8, 12

a)

Yes

b)

No

36.

State if the three numbers can be the measures of the sides of a triangle. 10, 6, 8

a)

No

b)

Yes

37.

Two sides of a triangle have the following measures. Find the range of possible measures for the third side. 12, 12

a)

0 < x < 24

b)

3 < x < 24

c)

1 < x < 20

d)

4 < x < 23

e)

0 < x < 23

38.

Two sides of a triangle have the following measures. Find the range of possible measures for the third side. 7, 9

a)

5 < x < 13

b)

5 < x < 16

c)

2 < x < 14

d)

None of these

e)

2 < x < 16

39.

Order the sides of the triangle from shortest to longest. Triangle UST has angle measures S = 60°, T = 35°, and U = 85°. Choose the correct order of sides.

a)

UT, TS, US

b)

US, UT, TS

c)

UT, US, TS

d)

TS, US, UT

e)

TS, UT, US

40.

Order the sides of the triangle from shortest to longest. Triangle HGF has angle measures H = 48°, F = 56°, and G = 76°. Choose the correct order of sides.

a)

HG, HF, GF

b)

GF, HF, HG

c)

HF, GF, HG

d)

HF, HG, GF

e)

GF, HG, HF

41.

Order the angles in the triangle from smallest to largest. Triangle MNL has side lengths ML = 11, NL = 20, and MN = 21.

a)

None of these

b)

∠N, ∠L, ∠M

c)

∠L, ∠N, ∠M

d)

∠M, ∠N, ∠L

e)

∠N, ∠M, ∠L

42.

Order the angles in the triangle from smallest to largest. Triangle DEF has side lengths DF = 14, DE = 13, and EF = 8.

a)

∠D, ∠E, ∠F

b)

∠D, ∠F, ∠E

c)

None of these

d)

∠E, ∠F, ∠D

e)

∠F, ∠E, ∠D

43.

Solve for x. A right triangle has one acute angle labeled 50° and the other acute angle labeled x + 48°. All three angles of the triangle sum to 180°.

a)

−8

b)

8

c)

12

d)

−9

e)

6

44.

Each figure shows a triangle with one or more of its medians. Find IH if WH = 3.9.

a)

2.6

b)

7.8

c)

None of these

d)

5.2

e)

11.7

45.

Choose the congruence theorem that proves the two triangles are congruent based on the diagram showing an X-shaped pair of triangles with matching tick marks on two sides and the vertical angle at the intersection marked as congruent.

a)

HL

b)

SAS

c)

Not enough information

d)

SSS

e)

AAS

46.

Choose the congruence theorem that proves the two triangles drawn from a common vertex are congruent. The base of the right-hand triangle has a right-angle marker at the base, and the two slanted sides from the shared vertex have matching tick marks.

a)

Not enough information

b)

SAS

c)

HL

d)

None of these

e)

AAS

47.

State what additional information is required in order to know that the triangles are congruent for the reason AAS. The diagram shows quadrilateral FVUW with diagonal segments and one right-angle marker at V and U.

a)

None of these

b)

∠WVU ≅ ∠FUV

c)

UW ≅ VF

d)

WV ≅ FU or UW ≅ VF

e)

∠W ≅ ∠F or ∠WVU ≅ ∠FUV

48.

State what additional information is required in order to know that the triangles are congruent for the reason HL. The left figure is right triangle XYZ with a right-angle at Z and a tick mark on YZ; the right figure is right triangle GIH with a right-angle at I and a tick mark on IH.

a)

ZY ≅ IH

b)

∠Z ≅ ∠I or ∠X ≅ ∠G

c)

∠Y ≅ ∠H

d)

∠Z ≅ ∠I

e)

None of these

49.

State what additional information is required in order to know that the triangles are congruent for the reason AAS. The left figure shows triangle CDE with a right-angle at E and the right figure shows triangle QRP with a right-angle at P; two corresponding sides have tick marks.

a)

CD ≅ PQ or DE ≅ QR

b)

DE ≅ QR or EC ≅ RP

c)

∠D ≅ ∠Q

d)

∠C ≅ ∠P or ∠E ≅ ∠R

e)

∠D ≅ ∠Q or ∠E ≅ ∠R

50.

State what additional information is required in order to know that the triangles are congruent for the reason AAS. The left figure shows quadrilateral RSTT with a triangle RST having a tick mark on RS; the right figure shows triangle JKL with a tick mark on JL.

a)

∠T ≅ ∠J

b)

∠S ≅ ∠K

c)

None of these

d)

RT ≅ LJ

e)

∠R ≅ ∠L

51.

Write a rule to describe the transformation that maps the black figure to the blue figure on the coordinate grid.

a)

translation: 2 units right and 4 units down

b)

rotation 90° counterclockwise about the origin

c)

rotation 90° clockwise about the origin

d)

rotation 180° about the origin

e)

None of these

52.

Write a rule to describe the transformation that maps the black figure to the blue figure on the coordinate grid.

a)

rotation 90° counterclockwise about the origin

b)

reflection across the x-axis

c)

translation: 7 units left

d)

rotation 180° about the origin

e)

rotation 90° clockwise about the origin

53.

Write a rule to describe the transformation that maps the black quadrilateral to the blue quadrilateral on the coordinate grid.

a)

rotation 90° clockwise about the origin

b)

translation: 2 units up

c)

translation: 5 units left and 2 units up

d)

translation: 4 units left and 4 units up

e)

None of these

54.

Write a rule to describe the transformation that maps the black triangle to the blue triangle on the coordinate grid.

a)

translation: 4 units left and 2 units down

b)

translation: 2 units left

c)

reflection across x = 1

d)

rotation 90° clockwise about the origin

e)

rotation 180° about the origin

55.

Write a rule to describe the transformation that maps the black quadrilateral to the blue quadrilateral on the coordinate grid.

a)

translation: 3 units up

b)

rotation 180° about the origin

c)

translation: 2 units left

d)

translation: 3 units left

e)

None of these

56.

Write a rule to describe the transformation that maps the black triangle to the blue triangle on the coordinate grid.

a)

translation: 2 units right and 3 units down

b)

rotation 180° about the origin

c)

None of these

d)

translation: 2 units right and 4 units down

e)

reflection across the x-axis

57.

Find the coordinates of the vertices of figure F–G–H–I after the transformation translation: 1 unit left and 1 unit down.

a)

F(−4, −2), G(−3, 3), H(−1, 3), I(−2, 0)

b)

F(2, −3), G(3, 2), H(5, 2), I(4, −1)

c)

F(3, −4), G(−2, −3), H(−2, −1), I(1, −2)

d)

G(−1, 2), H(−3, 2), I(−2, −1), F(0, −3)

e)

F(−5, −4), G(−4, 1), H(−2, 1), I(−3, −2)

58.

Find the coordinates of the vertices of triangle B–C–D after the transformation translation: 5 units right and 1 unit up.

a)

B(2, −1), C(4, 0), D(5, −4)

b)

B(−5, −1), C(−3, 0), D(−2, −4)

c)

None of these

d)

B(3, 2), C(1, 1), D(0, 5)

e)

C(−1, 1), D(0, 5), B(−3, 2)

59.

State the most specific name for the figure shown: a quadrilateral with all sides marked equal and all angles marked right angles.

a)

None of these

b)

square

c)

isosceles trapezoid

d)

kite

e)

quadrilateral

60.

State the most specific name for the figure shown: an irregular four-sided polygon with no parallel sides indicated.

a)

None of these

b)

trapezoid

c)

isosceles trapezoid

d)

kite

e)

quadrilateral

61.

State the most specific name for the figure shown: a four-sided figure with opposite sides both parallel (parallel marks shown).

a)

parallelogram

b)

quadrilateral

c)

isosceles trapezoid

d)

kite

e)

None of these

62.

State the most specific name for the figure shown: a four-sided figure with only one pair of parallel sides indicated.

a)

parallelogram

b)

None of these

c)

kite

d)

trapezoid

e)

isosceles trapezoid

63.

Solve for x in the quadrilateral K–L–M–N where the interior angles are labeled 96°, 67°, 95°, and 35x − 3°. Choose the value of x.

a)

6

b)

4

c)

8

d)

3

e)

None of these

64.

Solve for x in the trapezoid V–W–X–Y with consecutive angles labeled 60°, 120°, and 31x − 4°. Choose the value of x.

a)

7

b)

1

c)

5

d)

3

e)

4

65.

Solve for x. Each figure is a parallelogram. In parallelogram ABCD, diagonals intersect at Q with segments BQ and QD labeled BQ = 4x + 7 and QD = 6x − 1. Choose the value of x.

a)

4

b)

0

c)

6

d)

3

e)

8

66.

Solve for x. Each figure is a parallelogram. In parallelogram WXYZ with diagonal XZ, point S is the intersection of diagonals with segments XS = 12 and SZ = 2x − 2. Choose the value of x.

a)

None of these

b)

4

c)

0

d)

2

e)

1

67.

Use the diagram of quadrilateral FGDE. Angle at F is 35°, the angle at E is 120°, and the segment on FE is labeled 2x + 25. Solve for x.

a)

0

b)

11

c)

9

d)

6

e)

4

68.

Use the diagram of trapezoid XYZW with right side YZ. The top angles at X and Y are 40° and 92°. The bottom right segment on YZ is labeled 5x − 12. Solve for x.

a)

12

b)

None of these

c)

10

d)

7

e)

4

69.

Solve for x. Each figure is a trapezoid with the midsegment included. In trapezoid SRQP, the bases are SP = 44 and RQ = 16, and the midsegment ML is labeled 2x + 10.

a)

2

b)

4

c)

6

d)

10

e)

8

70.

Solve for x. Each figure is a trapezoid with the midsegment included. In trapezoid TUVW, the bases are TW = 21 and UV = 17, and the midsegment LM is labeled −2x + 19.

a)

8

b)

None of these

c)

11

d)

2

e)

0

71.

Find the length of the diagonal indicated for each trapezoid. In trapezoid XYWV, diagonal XV = 6.2. Find diagonal YW.

a)

6.2

b)

7.7

c)

None of these

d)

5.4

e)

6.7

72.

Find the length of the diagonal indicated for each trapezoid. In trapezoid KJLM, diagonal KM = 8.8. Find diagonal JL.

a)

11.1

b)

12.1

c)

None of these

d)

8.8

e)

9.2

73.

Solve for x. In the kite WXYZ, the marked sides are congruent, the top segment WX is labeled 2x + 11, and the right side is labeled 11.

a)

9

b)

5

c)

0

d)

10

e)

6

74.

Solve for x. In the kite EFGH, the marked sides are congruent. Angle at H is 108°, angle at G is 83°, and the left side near F is labeled 10x − 4. Solve for x.

a)

2

b)

None of these

c)

12

d)

9

e)

4

75.

Find the area of each. The trapezoid has bases labeled 4.8 in and 1.2 in, with a dashed height of 3 in. Find the area.

a)

36.4 in²

b)

18.2 in²

c)

4.5 in²

d)

9 in²

e)

None of these

76.

Find the area of each. The kite has diagonals labeled 8 km and 4.5 km (dashed). Find the area.

a)

4.1 km²

b)

18 km²

c)

9.4 km²

d)

36 km²

e)

9 km²

77.

Find the surface area of each figure. Round your answers to the nearest hundredth, if necessary. Use the composite pyramid shown with edges labeled 7.3 yd, 6 yd, and 4.1 yd, and dashed slant heights indicated.

a)

None of these

b)

171 yd²

c)

121.8 yd²

d)

165 yd²

e)

201 yd²

78.

Find the surface area of each figure. Round your answers to the nearest hundredth, if necessary. Use the composite pyramid shown with base edges 5 cm and an upper slant height labeled 10.3 cm; dashed internal heights indicated.

a)

128 cm²

b)

69 cm²

c)

81 cm²

d)

152 cm²

e)

146 cm²

79.

Find the area of each. Use the composite rectangle shown with long side labeled 10 mi and short side labeled 1 mi; smaller inner rectangle segments indicated at 10 mi and 2 mi.

a)

37 mi²

b)

54 mi²

c)

67 mi²

d)

53 mi²

e)

64 mi²

80.

Find the area of each. Use the polygon shown with side lengths labeled 12, 10 in, and 8.3 in; dashed diagonals and an interior point indicated.

a)

849 in²

b)

None of these

c)

1050 in²

d)

1098 in²

e)

808 in²

81.

Find the volume of each figure. Round your answers to the nearest hundredth, if necessary. The sphere has radius 5.4 km.

a)

76.13 km³

b)

659.58 km³

c)

None of these

d)

82.45 km³

e)

90.28 km³

82.

Find the volume of each figure. Round your answers to the nearest hundredth, if necessary. Use the right trapezoidal prism shown with edges labeled 4 ft, 6.1 ft, 11 ft, and 7 ft; dashed height indicated.

a)

164 ft³

b)

183 ft³

c)

129 ft³

d)

None of these

e)

271 ft³

83.

Find the volume of each figure. Round your answers to the nearest hundredth, if necessary. Use the truncated prism shown with top edges 10 ft and 6 ft, bottom edges 3 ft and 4 ft, and a vertical height of 3.7 ft; dashed interior shown.

a)

95.1 ft³

b)

None of these

c)

128.3 ft³

d)

166.5 ft³

e)

182 ft³

84.

Find the volume of each figure. Round your answers to the nearest hundredth, if necessary. The solid has a circular base with radius 8 cm and slant segment labeled 16 cm.

a)

537.75 cm³

b)

1263.3 cm³

c)

557.49 cm³

d)

1072.33 cm³

e)

844.43 cm³

85.

The polygons in each pair are similar. Find the missing side length. Two rectangles are shown: one is 6 by 8 and the other is 6 by 15 with one side marked ?. Find the missing side.

a)

20

b)

14

c)

12

d)

27

e)

21

86.

The polygons in each pair are similar. Find the missing side length. Two triangles are shown: larger has base 12 and another side 14; smaller has base 6 and another side 7; find the missing corresponding side on the larger triangle.

a)

10

b)

13

c)

None of these

d)

7

e)

8

87.

Find the missing length. The triangles in each pair are similar. In triangle ABC similar to triangle KLC inside the big triangle, sides along the left are 27 and 24, and the interior segment near the top is 9. Find the missing segment marked L.

a)

11

b)

6

c)

None of these

d)

8

e)

10

88.

Find the missing length. The triangles in each pair are similar. ΔEFG ~ ΔEVW. The segments labeled are EV = 36, EW = 154, and VW = 42. Find the missing length marked on segment FG.

a)

193

b)

133

c)

None of these

d)

188

e)

132

89.

State if the triangles in each pair are similar. If so, state how you know they are similar and complete the similarity statement. ΔUVW ~ ______. The top triangle shows one angle with a single arc and another with a double arc; the bottom triangle shows the same markings.

a)

not similar

b)

similar; SAS similarity; ΔBCD

c)

similar; AA similarity; ΔDCB

d)

similar; AA similarity; ΔBCD

e)

None of these

90.

State if the triangles in each pair are similar. If so, state how you know they are similar and complete the similarity statement. ΔABC ~ ______. One triangle has sides 25 and 40 around an included marked angle; the other has sides 5 and 8 around the included marked angle.

a)

similar; SAS similarity; ΔLNM

b)

similar; SSS similarity; ΔLNM

c)

similar; SAS similarity; ΔLMN

d)

similar; AA similarity; ΔNLM

e)

not similar

91.

State if the triangles in each pair are similar. If so, state how you know they are similar and complete the similarity statement. ΔFGH ~ _____. One triangle has sides 18, 22, and 26; the other has sides 81, 99, and 117.

a)

similar; SSS similarity; ΔCDE

b)

similar; SAS similarity; ΔDCE

c)

similar; SAS similarity; ΔCED

d)

similar; SSS similarity; ΔECD

e)

not similar

92.

State if the triangles in each pair are similar. If so, state how you know they are similar and complete the similarity statement. ΔTSR ~ ______. The segments in one triangle are marked 108 and 62; the other triangle has segments 47 and 28 with a third side 62 shown.

a)

similar; SAS similarity; ΔTMN

b)

similar; SSS similarity; ΔTMN

c)

not similar

d)

similar; SAS similarity; ΔNTM

e)

similar; AA similarity; ΔTMN

93.

Find the value of each trigonometric ratio. In the right triangle, the right angle is at B. The hypotenuse AC is labeled 50, the leg BC is labeled 14, and the leg BA is labeled 48. Find cos C.

a)

725\frac{7}{25}

b)

2425\frac{24}{25}

c)

724\frac{7}{24}

d)

None of these

e)

2524\frac{25}{24}

94.

Find the value of each trigonometric ratio. Triangle ZXY has a right angle at Y, with sides YZ = 6, YX = 8, and ZX = 10. Find tan X.

a)

54\frac{5}{4}

b)

34\frac{3}{4}

c)

35\frac{3}{5}

d)

45\frac{4}{5}

e)

None of these

95.

Find the measure of the indicated angle to the nearest degree. In the right triangle, the hypotenuse is 56 and the leg opposite the indicated angle is 42. Find the indicated angle.

a)

41°

b)

49°

c)

53°

d)

19°

e)

37°

96.

Find the length of each arc. Round your answers to the nearest tenth. A circle has a central angle of 315° and radius 9 miles. Find the arc length.

a)

222.7 mi

b)

None of these

c)

49.5 mi

d)

33.5 mi

e)

236.3 mi

97.

Find the length of each arc. Round your answers to the nearest tenth. A circle has a central angle of 210° and radius 15 inches. Find the arc length.

a)

55.0 in

b)

24.9 in

c)

412.3 in

d)

9.9 in

e)

34.8 in

98.

Find the area of each sector. Round your answers to the nearest tenth. A sector has a central angle of 315° and radius 11 cm. Find the area of the sector.

a)

332.6 cm²

b)

88.5 cm²

c)

None of these

d)

22.3 cm²

e)

18.3 cm²

99.

Find the area of each sector. Round your answers to the nearest tenth. A sector has a central angle of 315° and radius 14 yd. Find the area of the sector.

a)

18.3 yd²

b)

538.8 yd²

c)

3.9 yd²

d)

86.4 yd²

e)

4.7 yd²

100.

Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent. At point L on a circle, a tangent makes an 80° angle with a chord. Find the measure of the intercepted arc indicated by ?.

a)

225°

b)

None of these

c)

180°

d)

200°

e)

185°

101.

Complete each congruence statement by naming the corresponding angle or side. ΔPQR ≅ ΔLJK. In the left triangle, vertices are labeled Q, R, P; in the right triangle, vertices are labeled L, J, K. Identify the part that corresponds to ∠R.

a)

∠J

b)

∠L

c)

KL

d)

LK

e)

JK

102.

Complete each congruence statement by naming the corresponding angle or side. ΔFGH ≅ ΔFGJ. Identify the part that corresponds to ∠H.

a)

∠FGJ

b)

None of these

c)

∠G

d)

∠JFG

e)

JF

103.

Solve for x on the line shown: points L, M, N are collinear with LM labeled 3x + 3, MN labeled 11, and LN labeled 10x.

a)

2

b)

12

c)

1

d)

7

e)

0

104.

Solve for x on the line shown: points V, U, T are collinear with VU labeled x, UT labeled 2x − 4, and VT labeled 14.

a)

6

b)

3

c)

7

d)

5

e)

−6

105.

Find the midpoint of the line segment with the given endpoints (−8, 6) and (2, 0).

a)

(1 1/2, −8)

b)

(12, −6)

c)

(−3, 3)

d)

None of these

e)

(−1, 1)

106.

Find the midpoint of the line segment with the given endpoints (−9, −10) and (−2, −9).

a)

(−5 1/2, −9 1/2)

b)

(−3 1/2, −1/2)

c)

(−9 1/2, −5 1/2)

d)

(−5, −4 1/2)

e)

(5, −8)

107.

Find the distance between the points (7, −6) and (3, 0).

a)

2√13

b)

5√2

c)

4

d)

2√34

e)

√10

108.

Find the distance between the points (7, 2) and (−7, −8).

a)

√6

b)

2√74

c)

2√2

d)

2√6

e)

6

109.

m∠GHD = 34° and m∠GHI = 174°. Find m∠DHI.

a)

140°

b)

128°

c)

162°

d)

None of these

e)

95°

110.

m∠JIH = 180° and m∠RIH = 160°. Find m∠JIR.

a)

20°

b)

27°

c)

28°

d)

22°

e)

24°

111.

Find the measure of angle b in the diagram where intersecting lines show a 33° angle adjacent to angle b.

a)

21°

b)

57°

c)

147°

d)

33°

e)

159°

112.

Find the measure of angle b in the diagram with multiple rays from a point; one central angle is labeled 48°.

a)

None of these

b)

48°

c)

66°

d)

42°

e)

45°

113.

Find the value of x given a straight angle diagram where one angle is 65° and the adjacent angle is labeled (2x + 5)°.

a)

13

b)

14

c)

None of these

d)

11

e)

15

114.

Find the value of x in the diagram where an angle is 146° and the adjacent angle is labeled (x + 5)°.

a)

35

b)

29

c)

34

d)

31

e)

32

115.

Find the interior angle sum for each polygon. The figure shown is a hexagon. Round your answer to the nearest tenth if necessary.

a)

900°

b)

None of these

c)

1440°

d)

540°

e)

360°

116.

Find the interior angle sum for each polygon. The figure shown is a pentagon. Round your answer to the nearest tenth if necessary.

a)

720°

b)

540°

c)

1440°

d)

None of these

e)

900°

117.

Find the measure of one interior angle in each regular polygon. The figure shown is a regular 7‑gon. Round your answer to the nearest tenth if necessary.

a)

120°

b)

128.6°

c)

None of these

d)

90°

e)

144°

118.

Find the measure of one interior angle in each regular polygon. The figure shown is a regular pentagon. Round your answer to the nearest tenth if necessary.

a)

120°

b)

140°

c)

90°

d)

None of these

e)

108°

119.

Find the measure of one exterior angle in each regular polygon. The figure shown is a regular hexagon. Round your answer to the nearest tenth if necessary.

a)

32.7°

b)

60°

c)

72°

d)

90°

e)

None of these

120.

Find the measure of one exterior angle in each regular polygon. The figure shown is a square. Round your answer to the nearest tenth if necessary.

a)

60°

b)

45°

c)

51.4°

d)

40°

e)

None of these

121.

Find the slope of the line through each pair of points (12, −6) and (−6, 5).

a)

−3/2

b)

−11/18

c)

11/18

d)

None of these

e)

−18/11

122.

Find the slope of the line through each pair of points (20, 8) and (20, 3).

a)

0

b)

Undefined

c)

1/2

d)

−1/2

e)

−1/3

123.

Write the slope‑intercept form of the equation of the line shown on the coordinate plane.

a)

y = −4/5 x − 2

b)

y = −2x + 4/5

c)

y = 2/5 x − 2

d)

y = 4/5 x − 2

e)

y = 1/5 x − 2

124.

Write the slope‑intercept form of the equation of the line shown on the coordinate plane.

a)

y = x + 5

b)

y = 5x + 1

c)

None of these

d)

y = 4x + 5

e)

y = −x + 5

125.

Write the slope‑intercept form of the equation of the line described: through (−3, 1), parallel to x = 0.

a)

x = 3

b)

y = 3/2

c)

y = x − 3/2

d)

x = −3

e)

None of these

126.

Write the slope‑intercept form of the equation of the line described: through (2, 5), parallel to y = x + 1.

a)

y = −2x + 3

b)

y = 3x − 2

c)

y = 2x + 3

d)

None of these

e)

y = −x + 3

127.

Write the slope‑intercept form of the equation of the line described: through (−4, −5), perpendicular to y = −4/7 x + 2.

a)

y = 7/4 x − 2

b)

y = −7/4 x + 2

c)

y = −2x − 7/4

d)

None of these

e)

y = 2x − 7/4

128.

Write the slope‑intercept form of the equation of the line described: through (−2, 0), perpendicular to y = 1/2 x − 3.

a)

y = 2x − 4

b)

y = −2x − 4

c)

y = −x − 4

d)

y = −4x + 2

e)

None of these

129.

Write the slope‑intercept form of the equation of each line: 11x + 8y = −24.

a)

y = −3x − 1/4

b)

y = −11/8 x − 3

c)

y = 1/4 x − 3

d)

y = x − 3

e)

y = −1/4 x − 3

130.

Write the slope‑intercept form of the equation of each line: 3x − 4y = 8.

a)

y = 3/4 x − 2

b)

y = −3/4 x − 2

c)

y = −2x − 5/4

d)

y = 1/2 x − 5/4

e)

y = −5/4 x − 2

131.

Find the measure of the angle indicated by the question mark in the parallel‑line diagram where one interior angle is 98°.

a)

None of these

b)

84°

c)

129°

d)

130°

e)

75°

132.

Find the measure of the angle indicated by the question mark in the parallel‑line diagram where an adjacent angle measures 53°.

a)

44°

b)

53°

c)

94°

d)

141°

e)

102°

133.

Solve for x. In the diagram, two horizontal lines marked as parallel are cut by a slanted transversal. The upper intersection angle is labeled 11x − 2, and the lower same-side interior angle is labeled 105°. Use the relationship of same-side interior angles formed by parallel lines.

a)

−5

b)

7

c)

None of these

d)

−4

e)

−7

134.

Solve for x. Two horizontal parallel lines are cut by a slanted transversal. The upper interior angle is labeled 17x − 6 and the lower same-side interior angle is labeled 7x − 6.

a)

3

b)

10

c)

None of these

d)

8

e)

−3

135.

State if the three numbers can be the measures of the sides of a triangle: 11, 8, 12.

a)

Yes

b)

No

136.

State if the three numbers can be the measures of the sides of a triangle: 10, 6, 8.

a)

No

b)

Yes

137.

Two sides of a triangle have the measures 12 and 12. Find the range of possible measures for the third side x.

a)

0 < x < 24

b)

3 < x < 24

c)

1 < x < 20

d)

4 < x < 23

e)

0 < x < 23

138.

Two sides of a triangle have the measures 7 and 9. Find the range of possible measures for the third side x.

a)

5 < x < 13

b)

5 < x < 16

c)

2 < x < 14

d)

None of these

e)

2 < x < 16

139.

Order the sides of the triangle from shortest to longest. Triangle UST has angle measures at the vertices: ∠S = 60°, ∠T = 35°, ∠U = 85°. List the sides in order from shortest to longest.

a)

UT, TS, US

b)

US, UT, TS

c)

UT, US, TS

d)

TS, US, UT

e)

TS, UT, US

140.

Order the sides of the triangle from shortest to longest. Triangle HGF has angle measures at the vertices: ∠H = 48°, ∠G = 76°, ∠F = 56°. List the sides in order from shortest to longest.

a)

HG, HF, GF

b)

GF, HF, HG

c)

HF, GF, HG

d)

HF, HG, GF

e)

GF, HG, HF

141.

Order the angles in the triangle from smallest to largest. Triangle MNL has side lengths MN = 21, NL = 20, and ML = 11. List the angles in order from smallest to largest.

a)

None of these

b)

∠N, ∠L, ∠M

c)

∠L, ∠N, ∠M

d)

∠M, ∠N, ∠L

e)

∠N, ∠M, ∠L

142.

Order the angles in the triangle from smallest to largest. Triangle DEF has side lengths DE = 13, DF = 14, and EF = 8. List the angles in order from smallest to largest.

a)

∠D, ∠E, ∠F

b)

∠D, ∠F, ∠E

c)

None of these

d)

∠E, ∠F, ∠D

e)

∠F, ∠E, ∠D

143.

Solve for x. A triangle has two base angles of 70° each, and the third angle is labeled 3x + 7.

a)

11

b)

−8

c)

−10

d)

−5

e)

−11

144.

Solve for x. In a right triangle, the right angle is at the bottom right, the acute angle at the top is 50°, and the acute angle at the bottom left is labeled x + 48.

a)

−8

b)

8

c)

12

d)

−9

e)

6