Geometry Study Guide II Semester Exam

1. Review notes taken in class2. Review the theorems and postulates 3. Review quizzes4. Review test5. Review vocabulary words6. Solve the study guide.

Lesson 6.1

1. Describe the figure using as many of these words as possible: rectangle, trapezoid, square, quadrilateral, parallelogram, rhombus.

trapezoid, quadrilateral

rhombus, quadrilateral

quadrilateral, parallelogram

square, parallelogram

2. Classify the figure in as many ways as possible.

rectangle, trapezoid, quadrilateral, parallelogram, rhombus

rectangle, square, quadrilateral, parallelogram, rhombus

rectangle, quadrilateral, parallelogram

rhombus, trapezoid, quadrilateral, parallelogram

3. Identify the quadrilateral which has all sides and angles congruent.

square

rhombus

parallelogram

trapezoid

4. Which statement is true?

All rectangles are squares.

All quadrilaterals are squares.

All quadrilaterals are parallelograms.

All parallelograms are quadrilaterals.

5. Determine the most precise name for the quadrilateral with vertices at A(–7, –2), B(0, 2), C(4, –5), and D(–3, –9).

square

rhombus

kite

rectangle

Lesson 6.2

Find the value of the variables in the parallelogram.

x = 32°, y = 26°, z = 122°

x = 61°, y = 16°, z = 148°

x = 26°, y = 32°, z = 122°

x = 16°, y = 61°, z = 148°

2. For the parallelogram below, m∠1 = m∠3 = 5x, m∠2 = 3x – 60, and m∠4 = x. Find the value of x. The diagram is NOT to scale.

30

120

60

56

3. Parallelogram DEFG is below. DH = y + 4, HF = 3x – 1, GH = 2y, and HE = 3x + 2. Find the values of x and y.

x = 14, y = 11

x = 4, y = 7

x = 7, y = 4

x = 11, y = 14

4. Find the value of x.

3

14

11

33

5. Parallelogram DEFG is below. DH = x + 1, HF = 2y, GH = 2x – 2, and HE = 2y + 2. Find the values of x and y.

x = 3, y = 5

x = 8, y = 6

x = 5, y = 3

x = 6, y = 8

Lesson 6.3

Which description would NOT guarantee that the figure was a square?

a parallelogram with perpendicular diagonals

both a rectangle and a rhombus

a quadrilateral with all sides and all angles congruent

a quadrilateral with all right angles and all sides congruent

2. Which statement can be used to determine whether quadrilateral XYZW must be a parallelogram?

≅ and ≅

≅ and ≅

≅ and ≅

XW = WZ and XY = YZ

3. If m∠B = m∠D = 72, find m∠C so quadrilateral ABCD is a parallelogram.

108

162

72

18

4. Find values of x and y for which ABCD must be a parallelogram.

x = 11, y = 47

x = 47, y = 47

x = 36, y = 11

x = 47, y = 11

5. Complete ≅ _____ for parallelogram EFGH. Then state a definition or theorem as the reason.

; because the angles of a parallelogram bisect each other

; because the diagonals of a parallelogram bisect each other

; because the diagonals of a parallelogram bisect each other

; because the angles of a parallelogram bisect each other

Lesson 6.4

DEFG is a rectangle. Find the value of x and the length of each diagonal if DF = 6x – 1 and EG = x + 7.

x = , DE = FG = 8

x = 1, DF = EG =

x = , DF = EG = 8

x = 1, DE = FG =

2. DEFG is a rectangle. Find the value of x and the length of each diagonal if DF = 2x – 1 and EG = x + 3.

x = 4, DF = EG = 7

x = 2, DF = 3, EG = 5

x = , DF = , EG =

x = 7, DF = 13, EG = 10

3. Determine whether each quadrilateral can be a parallelogram. If not, write impossible.a. Two adjacent angles are right angles, but the quadrilateral is not a rectangle.b. All of the angles are congruent.

a. impossible; b. parallelogram

a. parallelogram; b. parallelogram

a. parallelogram; b. impossible

a. impossible; b. impossible

4. Must the figure be a parallelogram? Explain.

Yes; there are four angles congruent in pairs.

No; the left side is not parallel to the right side.

No; the two isosceles triangles have different base angles, so the two unmarked base angles do not have to be congruent.

Yes; the parallelogram is divided into two congruent triangles.

5. Must the figure be a parallelogram? Explain.

Yes; one pair of opposite sides is parallel.

No; all four sides are not congruent.

Yes; both pairs of opposite sides are congruent.

No; only one pair of opposite sides is congruent.

Lesson 6.5

∠J and ∠M are base angles of isosceles trapezoid JKLM. If m∠J = 11x + 4, m∠K = 15x + 5, and ∠M = 10x + 9, find the value of x.

5

13

–

2. If you draw two noncongruent kites, which statement is true?

It is possible to draw two noncongruent kites with the sides of one congruent to the sides of the other.

It is possible to draw two noncongruent kites with the diagonals of one kite perpendicular, and the diagonals of the other kite not perpendicular.

It is possible to draw two noncongruent kites with the diagonals of one congruent to the diagonals of the other.

It is possible to draw two noncongruent kites with the angles of one congruent to the angles of the other.

3. What type of symmetry does a square have?

point symmetry

rotational symmetry

line symmetry

all of the above

4. Write a paragraph proof to show that the base angles of an isosceles trapezoid are congruent.

ABDC is isosceles, so ≅ and || . Construct and perpendicular to . Then ≅ . Also ΔAPC ≅ ΔBQD by HL, and ∠D ≅ ∠C by the Isosceles Triangle Theorem. Since

complements of congruent angles are congruent, ∠A ≅ ∠B.

ABDC is isosceles, so ≅ and || . Construct and perpendicular to . Then ≅ . Also ΔAPC ≅ ΔBQD by SAS, and ∠D ≅ ∠C by CPCTC. Since supplements of congruent angles

are congruent, ∠A ≅ ∠B.

ABDC is isosceles, so ≅ and || . Construct and perpendicular to Then ≅ . Also ΔAPC ≅ ΔBQD by SAS, and ∠D ≅ ∠C by the Isosceles Triangle Theorem. Since

complements of congruent angles are congruent, ∠A ≅ ∠B.

ABDC is isosceles, so ≅ and || . Construct and perpendicular to . Then ≅ . Also ΔAPC ≅ ΔBQD by HL, and ∠D ≅ ∠C by CPCTC. Since supplements of congruent angles

are congruent, ∠A ≅ ∠B.

5. ∠J and ∠M are base angles of isosceles trapezoid JKLM. If m∠J = 21x + 4, m∠K = 12x – 8, and ∠M = 14x + 10, find the value of x.

2

–

–9

Lesson 6.6

One side of a kite is 4 cm less than three times the length of another. If the perimeter is 84 cm, find the length of each side of the kite. Round your answer to the nearest tenth.

46 cm, 38 cm

23 cm, 19 cm

23 cm, 61 cm

11.5 cm, 30.5 cm

2. ∠J and ∠M are base angles of isosceles trapezoid JKLM. If m∠J = 11x + 4, m∠K = 15x + 5, and ∠M = 10x + 9, find the value of x.

5

13

–

3. What type of symmetry does a square have?

point symmetry

rotational symmetry

line symmetry

all of the above

4. ∠J and ∠M are base angles of isosceles trapezoid JKLM. If m∠J = 21x + 4, m∠K = 12x – 8, and ∠M = 14x + 10, find the value of x.

2

–

–9

5. Which of these descriptions would NOT guarantee that the figure was a kite?

a quadrilateral with perpendicular diagonals

a quadrilateral with one diagonal that bisects opposite angles and the other diagonal that does not

a quadrilateral with perpendicular diagonals, only one of which bisects the other

a quadrilateral with exactly two distinct pairs of congruent adjacent sides

Lesson 8.1

Find the area.

613 square units

294 square units

588 square units

84 square units

2. A triangle has side lengths of 8 cm, 11 cm, and cm. Classify the triangle.

right

obtuse

acute

3. How many of these triples could be sides of a right triangle: (27, 36, 45), (12, 17, 20), (24, 32, 40), (14, 48, 50)?

4 triples

3 triples

2 triples

1 triple

4. Use the converse of the Pythagorean theorem to determine which three numbers could represent the sides of a right triangle.

64, 73, 98

65, 72, 97

65, 71, 97

64, 72, 96

5. Find the length of the leg of the right triangle. Leave your answer in simplest radical form.

48

288

Lesson 8.2

Find the value of x.

6

12

24

12

2. The hypotenuse of a 30°–60°–90° triangle is 3. Find the perimeter.

3 +3

+

+

2 + 2

3. Compare the quantity in Column A with the quantity in Column B.

The quantity in Column A is greater.

The quantity in Column B is greater.

The two quantities are equal.

The relationship cannot be determined based on the given information.

4. In ΔABC, ∠A is a right angle and m∠B = 60. If AB = 20 ft, find BC. If necessary, round your answer to the nearest tenth.

10 ft.

40 ft

20 ft

ft

5. Find the value of the variable.

14

Lesson 8.3

A large flagpole is 193 feet tall. On a particular day at noon it casts a 159-foot shadow. What is the sun's angle of elevation at that time? Round to the nearest tenth.

50.5°

39.5°

34.5°

none of these

2. Find the measure of the marked acute angle to the nearest degree.

64°

26°

35°

116°

3. Find the value of the variable to the nearest hundredth.

5.28 cm

0.32 cm

3.13 cm

5.12 cm

4. Find the measure of the marked acute angle to the nearest degree.

25°

30°

120°

60°

5. A large totem pole near Kalama, Washington, is 100 feet tall. On a particular day at noon it casts a 219-foot shadow. What is the sun's angle of elevation at that time? Round to the nearest tenth.

27.2°

62.8°

65.5°

none of these

Lesson 8.4

Find the value of x to the nearest degree.

68

22

24

66

2. Sean and Jackie made a shady area by stretching a bedspread over a clothesline. The bedspread was 2.4 m long and made an angle of 52° with the ground where it was anchored at each side. How wide was the shady area?

0.3 m

1.5 m

1.3 m

2.5 m

3. Find the value of x to the nearest tenth.

14.4

6.3

7.8

3.1

4. Liola drives 130 m up a hill that has a slope of 7°. What horizontal distance, to the nearest hundredth of a meter, has she covered?

129.03 m

15.84 m

15.96 m

130.97 m

5. Find the ratio for cos x.

2

Lesson 10.1

Find the area.

102.9 yd2

205.8 yd2

35.35 yd2

105.5 yd2

2. Find the area of a parallelogram with vertices at P(–8, –3), Q (–7, 3), R(–9, 3), and S(–10, –3).

12 square units

6 square units

18 square units

none of these

3. Laura wants to paint a wall in her attic. The wall is a triangle with a base of 8 feet and a height of 9 feet. What is the area of the wall?

37 ft2

72 ft2

73 ft2

36 ft2

4. Find the area of a parallelogram with vertices at A(–9, 5), B(–8, 10), C(0, 10), and D(–1, 5).

30 square units

40 square units

20 square units

none of these

5. Find the area of a triangle with vertices at D(2, 0), E(–1, 0), and F(2, –7).

21 square units

8.5 square units

20 square units

10.5 square units

10.2

Find the area of kite ABCD if BD = 48 cm, AB = 25 cm, and BC = 26. The kite is not drawn to scale.

289 cm2

70 cm2

816 cm2

408 cm2

3. Find the area.

840 square units

1088 square units

544 square units

538 square units

4. Find the area of the rhombus.

378 ft2

189 ft2

78 ft2

39 ft2

5. Find the area of the rhombus to the nearest tenth.

361.3 square units

278.3 square units

437.8 square units

366.0 square units

10.3

Find the area of the regular polygon. Round your answer to the nearest tenth.

40.0 in.2

220.5 in.2

67.6 in.2

110.2 in.2

2. Find the area of the regular polygon. Round your answer to the nearest tenth.

314.4 cm2

60.5 cm2

121 cm2

628.7 cm2

3. Find the area of the regular polygon. Round your answer to the nearest tenth.

173.8 in.2

105.9 in.2

48.0 in.2

347.7 in.2

4. If a regular hexagon with 7-cm sides has an area of 42 cm2, what is the length of the apothem?

2 cm

1.5 cm

3 cm

6 cm

5. Find the area of a regular hexagon with an apothem 17.3 miles long and a side 20 miles long.

956 mi2

1038 mi2

1352 mi2

1124 mi2

Lesson 11.2

Use formulas to find the lateral area and the surface area of the prism. Show your answer to the nearest hundredth.

1246.51 m2; 1426.51 m2

186.00 m2; 2790.00 m2

144.00 m2; 5580.00 m2

1432.51 m2; 1612.51 m2

2. Use formulas to find the lateral area and the surface area of the prism. Show your answer to the nearest hundredth.

63.00 m2; 567.00 m2

36.00 m2; 1134.00 m2

479.22 m2; 533.22 m2

542.22 m2; 596.22 m2

3. Use a net to find the surface area of the prism.

465 m2

720 m2

918 m2

930 m2

4. Find the surface area of the cylinder to the nearest whole number.

79 m2

16 m2

25 m2

158 m2

5. Find the surface area of the cylinder in terms of π.

145.6π m2

194.6π m2

243.6π m2

170.8π m2

Lesson 11.3

Find the volume of the prism.

96 m3

192 m3

304 m3

30 m3

2. Find the volume of the cylinder in terms of π.

24π in.3

48π in.3

56π in.3

288π in.3

3. Cylinder A has radius 1 and height 4 and cylinder B has radius 2 and height 4. Find the ratio of the volumes of the two cylinders.

1 : 4

5 : 6

1 : 2

1 : 1

4. Find the volume of the composite space figure.

120 cm3

380 cm3

400 cm3

280 cm3

5. Find the height of the cylinder to the nearest tenth of an inch.

94.6 in.

96.6 in.

4.3 in.

4.1 in.

Lesson 11.4

Find the volume of the prism.

40.5 m3

162 m3

9 m3

81 m3

2. Cylinder A has radius 1 and height 4 and cylinder B has radius 2 and height 4. Find the ratio of the volumes of the two cylinders.

1 : 4

5 : 6

1 : 2

1 : 1

3. Find the volume of the composite space figure.

70 cm3

238 cm3

196 cm3

266 cm3

4. Find the volume of the composite space figure.

120 cm3

380 cm3

400 cm3

280 cm3

5. Find the volume of the prism.

96 m3

192 m3

304 m3

30 m3

Lesson 11.5

Find the volume of the square pyramid.

1050 ft3

3150 ft3

1575 ft3

9450 ft3

2. A machinist drilled a cone-shaped hole into a solid cube of metal as shown. If the cube has sides of length 7 centimeters, what is the volume of the metal after the hole is drilled? Use π ≈ 3.14 and round your answer to the nearest tenth.

235.3 cm3

235.2 cm3

253.2 cm3

223.3 cm3

3. A machinist drilled a cone-shaped hole into a solid cube of metal as shown. If the cube has sides of length 4 centimeters, what is the volume of the metal after the hole is drilled? Use π ≈ 3.14 and round your answer to the nearest tenth.

47.4 cm3

47.3 cm3

43.9 cm3

41.7 cm3

4. Compare the quantity in Column A with the quantity in Column B.

The quantity in Column A is greater.

The quantity in Column B is greater.

The two quantities are equal.

The relationship cannot be determined on the basis of the information given.

5. Find the volume of the cone. Use π ≈ 3.14.

8000.72 in.3

2464.19 in.3

2476.41 in.3

190.49 in.3

Lesson 11.6

Find the surface area of the sphere.

648π m2

72π m2

324π m2

1296π m2

2. A sphere has a volume of 288π ft3. Find the surface area of the sphere.

864π ft2

48π ft2

144π ft2

96π ft2

3. Find the surface area of a sphere that has a diameter of 4 cm.

64π cm2

π cm3

4π cm2

16π cm2

4. A sphere has a surface area of 900π ft2. Find the volume of the sphere.

300π ft3

4500π ft3

1200π ft3

13,500π ft3

5. Find the surface area of the sphere.

56π m2

784π m2

196π m2

392π m2

Lesson 12.1

In ΔMLK, MK = ML, and the perimeter is 32 cm. A, B, and C are points of tangency and LC = 4 cm. What is KA? (The diagram is not to scale.)

4 cm

14 cm

8 cm

12 cm

2. , , and are all tangent to circle O. If JA = 8, AL = 13, and CK = 11, what is the perimeter of ΔJKL? (The diagram is not to scale.)

32

64

45

53

3. Is line AB tangent to the circle? Why or why not? (The diagram is not to scale.)

yes; 92 + 122 = 152

no; 92 + 122 ≠ 142

no; 92 + 122 ≠ 152

yes; 92 + 122 = 142

4. is tangent to circle O at B. How close to the circle is point A? (The diagram is not to scale.)

3

4.5

6

7.5

5. , , and are all tangent to circle O. JA = 3, JL = 7, and the perimeter of ΔJKL = 26. What are JK and KL? (The diagram is not to scale.)

JK = 3, KL = 7

JK = 10, KL = 9

JK = 6, KL = 6

JK = 9, KL = 10

Lesson 12.2

CD = 60, OM = 18, and ON = 15. Find FN.

3

11

3

9

2. CM = 17, OM = 8, and ON = 9. Find EN.

4

16

4

4

3. Find the value of x when FG = 52, RQ = QS = 26, and OP = 10.

10

26

52

20

4. Find the value of x.

6.7

5.4

12.4

11.6

5. Find the value of x.

79

39

99

159

Lesson 12.3

1. Find the measure of ∠BAC.

76°

104°

142°

38°

2. Given: is tangent to circle O at C, m = 278, and m∠ACB = 35. Find m∠ACE.

104°

121.5°

110°

none of these

3. If m = 38, what is m∠YAC?

128°

109°

71°

218°

4. If m = 38, what is m∠YAC?

142°

71°

109°

52°

5. Given that ∠DAB and ∠DCB are right angles and m = 310, what is the measure of ∠ADB?

51°

65°

33°

115

Lesson 12.4

Solve for x.

27

9

3

4

2. A park maintenance person stands 19 m from a circular monument. If you assume her lines of sight form tangents to the monument and make an angle of 34°, what is the measure of the arc of the monument that her lines of sight intersect?

112

146

124

56

3. Determine AB.

4 or 9

4

1

1 or 6

4. Find the value of x if AB = 20, BC = 12, and CD = 13. (not drawn to scale)

18.8

16.5

13.4

14.9

5. Compare the quantity in Column A with the quantity in Column B.

The quantity in Column A is greater.

The quantity in Column B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Lesson 12.5

Write the standard equation for the circle with center (–2, 5) that passes through (1, 9).

(x – 2)2 + (y + 5)2 = 5

(x + 2)2 + (y – 5)2 = 5

(x + 2)2 + (y – 5)2 = 25

(x – 2)2 + (y + 5)2 = 25

2. A low-watt radio station can be heard only within a certain distance from the station. On the graph below, the circular region represents that part of the city where the station can be heard, and the center of the circle represents the location of the station. Which equation represents the boundary for the region where the station

can be heard?

(x – 4)2 + (y – 5)2 = 50

(x + 5)2 + (y – 5)2 = 59

(x + 5)2 + (y + 4)2 = 25

(x + 5)2 + (y – 5)2 = 25

3. Find the center and radius of (x + 8)2 + (y + 4)2 = 49.

(–8, –4); 7

(–4, 8); 7

(8, 4); 7

(–4, –8); 49

4. Write the standard equation for the circle with center (14, –48) that passes through (0, 0).

(x – 14)2 + (y + 48)2 = 2500

(x + 14)2 + (y – 48)2 = 2500

(x + 14)2 + (y – 48)2 = 50

(x – 14)2 + (y + 48)2 = 50

5. A small messenger company can only deliver within a certain distance from the company. On the graph below, the circular region represents that part of the city where the company delivers, and the center of the circle represents the location of the company. Which equation represents the boundary for the region where the

company delivers?

(x + 3)2 + (y – 1)2 = 49

(x + 3)2 + (y – 3)2 = 98

(x + 1)2 + (y – 3)2 = 98

(x + 3)2 + (y – 3)2 = 49

Lesson 9.1

Write a rule to describe a reflection over the y-axis.

(x, y) → (–x, y)

(x, y) → (–x, –y)

(x, y) → (x, –y)

(x, y) → (y, x)

2. Find the image of C under the translation described by each vector.a. ⟨4, 5⟩b. ⟨11, –8⟩

a. A; b. B

a. B; b. A

a. E; b. D

a. D; b. E

3. Find the vector that describes each translation.a. B → Db. E → C

a. ⟨7, 2⟩; b. ⟨5, 4⟩

a. ⟨–7, –2⟩; b. ⟨4, 5⟩

a. ⟨7, 2⟩; b. ⟨–4, –5⟩

a. ⟨2, 7⟩; b. ⟨–5, –4⟩

4. Which transformations are isometries?(I) parallelogram GHIJ → parallelogram UTSR

(II) hexagon EFGHIJ → hexagon VUTSRQ

(III) triangle GHI → triangle STR

II only

I, II, and III

III only

none of these

5. Which transformation is an isometry?

Lesson 9.2

1. Find the image of O(0, 0) after two reflections, first in y = 4, and then in x = –7.

(7, –4)

(–14, 8)

(8, –14)

(–4, 7)

2. If a point P(–1, –1) is reflected across the line y = –2, what are the coordinates of its reflection image?

(–1, 5)

(–1, –3)

(–3, –1)

(5, –1)

3. Which graph shows a triangle and its reflection image in the y-axis?

4. If a point P(1, –2) is reflected across the line x = 3, what are the coordinates of its reflection image?

(1, –4)

(1, 8)

(–7, –2)

(5, –2)

5. If a point P(–2, 1) is reflected across the line x = –1, what are the coordinates of its reflection image?

(0, 1)

(4, 1)

(–2, –3)

(–2, 1)

Lesson 9.5

Which transformation does NOT represent a dilation?

3. The dotted triangle is a dilation image of the solid triangle. What is the scale factor?

3

2

4

4. The dotted triangle is a dilation image of the solid triangle. What is the scale factor?

2

3

5. A blueprint for a house has a scale of 1 : 30. A wall in the blueprint is 7 in. What is the length of the actual wall?

210 ft

21 ft

17.5 ft

none of these

The END !!!!!