1

ADVANCED GEOMETRY: SPRING 2014 SEMESTER REVIEW

Determine if the following statements are True or False. to make it true.

If False, rewrite the statement

1)

Every quadrilateral is a parallelogram.

2)

If quadrilateral ABCD is a parallelogram, then AC

3)

If both pairs of opposite angles in a quadrilateral are congruent, then the quadrilateral is a parallelogram.

4)

If NMOP is a rectangle, then it is a parallelogram.

5)

If a quadrilateral has congruent diagonals, it is a rectangle.

6)

If a quadrilateral is a rhombus or a square, then the diagonals are perpendicular.

7)

If a quadrilateral has four right angles, then it is a rectangle.

BD .

8) The bases of an isosceles trapezoid are congruent. 9)

A square has all the properties of a parallelogram, a rectangle, a rhombus, and a trapezoid.

10) The median of a trapezoid is parallel to the bases and its length is one-half the sum of the lengths of the bases. 11) The diagonals of a trapezoid are congruent.

Use the figure at the right to answer the following questions. Quadrilateral ABCD is a parallelogram. 12)

If mBCD = 125, find mBAD .

A

B E

13)

If mBAC = 45, find mACD . C

14)

If mBEA = 135, find mAED .

15)

If mDAB = 2x - 10 and mADC = 3x, find mDAB .

16)

If mABD = 3x - 12 and mBDC = x + 40, find mABD .

17)

If BE = 5x + 2, AE = 7x - 8, and ED = 3x + 26, find EC.

D

2

Determine whether the given information is sufficient to prove Quadrilateral ABCD is a parallelogram. If so, state which quadrilateral property supports your conclusion. 18)

Point E is the midpoint of AC and BD.

19)

ABC = ADC

20)

BAC = DCA and ADC is supplementary to DCB .

21)

Diagonals AC and BD are congruent.

22)

DBC = ADB and AD = BC.

A

B E

D

C

Use the figure of Rectangle NOPQ to answer the following. 23)

If m1 = 26, find m 2, m 3, and m 4.

N

O 4

24)

If mONR = 4x - 5 and mRNQ = 5x - 4, find mNRO .

25)

If mOPQ = 6x - 18 and m OQP = 2x + 5, find mQRP .

R 2

1

26)

If NP = 4x - 60 and OQ = 30 - x, find NR.

27)

If OR = x + 5 and NP = 4x - 60, find QR.

Q

Use the figure of Rhombus ABCD to answer the following. 28)

Find mBCE

29)

Find mBEC

30)

Find AC.

31)

Find AD.

32)

Find mABD

B 59

E

A

12 cm

C

14 cm

D

Use the figure of Square ABCD to answer the following. 33)

If mAEB = 3x, find x.

34)

If mBAC = 9x, find x.

35)

If mDAC = 3x, find x.

36)

If AB = x 2 - 15 and BC = 2x, find x.

A

B E

D

C

3 P

3

Determine if the figure with the given vertices is best described as a quadrilateral, parallelogram, rectangle, rhombus, or square. 37)

K (4,8), L (0,9),

M (-2,1),

38)

G (12,0), H (6,-6),

N (2,0)

I (0,0),

J (6,6)

Answer the following given Isosceles trapezoid JKLM with bases JK and LM, and median ST. 39) If JL = 3x + 5 and KM = 40 - 2x, find JL. 40) If mJML = 9x + 4 and mJKL = x + 36, find mKLM . 41) If ST = 12x - 7, JK = 9X + 3, and LM = 17x - 41, find ST.

Simplify: 108 42)

43)

56

44)

3 200  3 50

45)

( 2 5 2)

Find x. 46)

x = ________

47)

x = _________

48)

AB = ______, BC = ____

A

x

3

x

30

12

8 3

4 B 49)

C

Using the figure below to write the ratios (leave as a reduced fraction): cos x = _______ sin x = _______

25

15

x

tan x = _______

20

30

100

100 50)

x = _________

30 x

51)

x = ________

x

4

For # 52 - 54, find the value of x. Leave as exact answer for #52. nearest degree and sides to the nearest tenth for #53, 54. 52)

53)

27

Round angles to the

54)

x

x

15

x

52 29

18 8 55)

Determine if a triangle with sides 2, 3, and 4 is acute, right, or obtuse.

56)

The lengths of the sides of a triangle are 4, 6, and 8.

57)

If the lengths of the legs of a right triangle are 3 and 5, find the length of the hypotenuse.

58)

If a rectangle that is 6 cm long has a diagonal that is 9 cm long, how long is the width?

59)

Find the tan 45 degrees =

61) The simplified form of

________.

Is the triangle a right triangle?

60) tan x = 0.5

x = __________.

72 is ___________.

62) The angle of depression from the top of a 120 foot lighthouse looking down on a ship is 44. How far is the ship from the lighthouse?

63)

A cat sitting 10 yards from the bottom of a tree is looking up at a bird’s nest. The angle of elevation is 70. How high up in the tree is the nest?

64)

A skateboard ramp is 50 feet long and is 10 feet tall at its highest point. Find the angle of elevation of the ramp.

65)

An airplane is flying at an altitude of 12,000 feet. The angle of depression from the airplane to a ground signal is 53. Find the direct line distance between the airplane and the ground signal, rounded to the nearest whole number.

5

CHAPTER 10 66)

Area = _____. Perimeter = 18

67)

Area = _____. Perimeter = 24

68)

Area = ______. Perimeter = 52

5 Regular 69)

Regular

Area = _____.

70)

Area = _______.

71)

Area = 20. x = ___.

6

x

6 2

5

4

10

72)

Circumference = 12 Area = _______.

73)

Area = 25 74) Radius = 10. Circumference = _______. Area of square = _______.

75)

Find the area of a regular hexagon with an apothem 6 m long.

76)

Find the area of the parallelogram below.

8 30 14

77) The area of ABC is 24 in2 . If AC = 6 in, find the area of Circle P below.

C

A

P

B

6

78) What is the circumference of a circle whose area is 144 cm 2 ?

79) What is the area of a circle whose circumference is 18 cm ?

80) Find the area of an equilateral triangle with side length 6 in.

81) Which solid does the net represent? Find the total surface area.

10 in 6 in 18 in

82)

Draw the top, front, left and right views for the figure shown.

Front 83)

A prism with a square base has ____ edges.

84)

A prism with an octagonal base has ____ lateral edges.

85)

A pyramid with a square base has ____ edges.

Assume the bases are regular polygons. 86)

AD = 4. LA = _______.

SA = _______. V = ________.

4 A 87)

V  2 4 0 3. Height = ______.

4

D

7

88)

r = 4. h = 8.

89)

Surface Area of a cube is 486.

90)

Volume of a cylinder is 240 with diameter 8. Height = _____.

91)

92)

LA = ____. SA = ____. V = _____.

V = _______.

h = 10. V = 270. diameter = ______.

LA = ____. SA = ____. 13

10 93)

r = 9. Surface Area = _________

94)

Volume = ________

95)

r = 5. h = 10.

LA = _____ SA = _____ . V = ______.

#95

For #96 - 99, use the picture at the right. 96)

Find the circumference for the base.

97)

Find the lateral area.

98)

Find the area of the base.

99)

Find the surface area.

20

10

8

Find the lateral area and the surface of each right prism. 100)

4

3

8

101)

8

4

4

The two right rectangular prisms shown below are similar.

7

5

102)

Find the ratio of the perimeters of the bases.

103)

What is the ratio of the surface areas?

104)

Suppose the volume of the smaller prism is 60 in3 .

Find the volume of the larger prism.

In each circle, O is the center. Find each measure.

mNP

105)

KM

106)

N M

XY

107) H

F G

O

O P

120

X

K

12 E

Q

_____________

108)

O

12 B

20 Y

M

_____________

_____________

Suppose a chord of a circle is 5 inches from the center and is 24 inches long. of the radius.

Find the length

9

109)

Suppose the diameter of a circle is 30 centimeters long and a chord is 24 centimeters long. Find the distance between the chord and the center of the circle.

Find the missing angle or the variable. 110)

111)

112)

113)

114)

115)

116)

m1 = ________

m7  _______

m2  ________

m8  _______

m3  ________

m9  _______

m4  ________

m10  _______

m5  ________

m11  _______

m6  ________

m12  _______

8 7

6

5 3

4

1 2 110

9 10

12

11

117) Find DC.

150

A 4

3

D

B 4 2 C Y

118)

80

Name an arc with a measure of 240.

X 60 20

E

Z W

A