Geometry Final Review Ch 6-11 and Ch 0 Chapter 6 Review 1.) Find the sum of the interior angle measures of a convex 11-gon. 2.) Find the measure of each interior angle of a regular 18-gon. 3.) Find the measure of each exterior angle of a regular 15-gon.

In , are diagonals. NW=12, PN=9, and Draw the diagrams and find the following measures. 4.) PL 5.) QRST is a parallelogram (diagram below). 6.) TQ

!PNWL PW and NL m∠WLP = 144°.

m∠PNW

7.)

8.) Three vertices of are . Find the coordinates of vertex D. 9.) Determine if QWRT must be a parallelogram. Justify your answer.

10.) Show that the quadrilateral with vertices is a parallelogram.

m∠T

!ABCD A 2,−6( ),B −1,2( ), and C 5,3( )

E −1,5( ),F 2,4( ),G 0,−3( ) and H −3,−2( )

11.) A slab of concrete is poured with diagonal spacers. In rectangle CNRT, CN=35ft, and NT=58ft. Find each length. a.) TR b.)

12.) The vertices of square ABCD are . Show that its diagonals are congruent perpendicular bisectors of each other.

13.) Given that AB=BC=CD=DA, what additional information is needed to conclude ABCD is a square? 14.) Determine if the conclusion is valid. If not tell what addition information is needed to make it valid.

Given: PQRS and PQNM are parallelograms. Conclusion: MNRS is a rhombus

CT

A 1,3( ),B 3,2( ),C 4,4( ) and D 2,5( )

MN ≅ NR

15.) Use the diagonals to determine whether a parallelogram with vertices is a rectangle, rhombus, or square. Give all the names that apply.

In kite HJKL to the right, Find each measure. 16.) 17.) In 18 and 19, the figures are isosceles trapezoids. 18.)

19.) XV=4.6 and WY=14.2. Find VZ.

20.) . Find LP.

A 2,7( ),B 7,9( ),C 5,4( ) and D 0,2( )

m∠KLP = 72° and m∠HJP = 49.5°.

m∠LHJ m∠PKL

m∠WZY = 61°. Find m∠WXY.

LP !NS; LM ≅ MN and PQ ≅ QS

Chapter 7 Review 21.) Find the slope of the line through the points

(-6, 4) and (6, -2).

22.) Solve the proportion:

23.) The ratio of the side lengths of a triangle is 5 : 7 : 2, and its perimeter is 112 ft. What is the length of the

longest side? 24.) Given that 28h=42k, find the ratio of h to k in simplest form. 25.) , solve for y. 26.) True or false? Two equiangular triangles are similar? Why?

x − 45

= 20x − 4

ΔDEF~ ΔCBA

27.) Verify that the triangles are similar. a.)

b.)

28.) Solve for x.

29.) Verify that

30.) Solve for PS and SR

DB ! AE

31.) Given that find the perimeter P and area A of Chapter 8 Review 32.) Find the geometric mean of 8 and 9. If

necessary, leave answer in simplest radical form.

33.) Find the geometric mean of 14 and 21. If necessary, leave answer in simplest radical form.

34.) Solve for x, y, and z. If necessary, leave answer in simplest radical form.

ΔLMN~ ΔQRS, ΔQRS.

35.) To estimate the height of a Douglas fir, Amy positions herself so that her lines of sight to the top and bottom of the tree form a angle. Her eyes are about 1.6m above the ground, and she is standing 7.8m from the tree. What is the height of the tree to the nearest tenth of a meter?

For 36-39, use the diagram on the right. 36.) If PS=6 and PT=9, solve for PR. 37.) Write a similarity statement comparing the three triangles. 38.) If TP=24, PR=6, solve for RS.

39.) Complete the equation:

40.) Solve for BC. Round to the nearest

thousandth.

41.) Solve for QR. Round to the nearest thousandth.

90°

ST( )2 = TP +PR( ) ?( )

42.) Solve for FD. Round to the nearest thousandth. Use special right triangles to complete 43– 51. Draw a diagram for each. Leave as a simplified radical. 43.)

44.) 45.)

46.)

47.) 48.) 49.)

50.)

51.) Find the value of x. Then find the value of AB, BC, and AC. Round each measure to the nearest unit.

sin30°

sin45°

cos60°

sin30°cos60°

sin45°

tan60°

tan45°

sin45°cos45°

52.) What is the distance between: If necessary, leave as a simplified radical. 53.) Find the unknown measures. Round lengths to nearest hundredth, and angle measures to the nearest

degree. 54.) An ice climber stands at the edge of a crevasse that is 115ft wide. The angle of depression from the edge

where she stands to the bottom of the opposite side is How deep is the crevasse at the point? Round to the nearest foot.

55.) An observer in a lighthouse is 69 foot above the water. He sights two boats in the water directly in front

of him. The angle of depression to the nearest boat is The angle of depression to the other boat is What is the distance between the two boats? Round to the nearest tenth of a foot.

8,10( ) and 3,0( )?

52°.

48°.22°.

For 56-60, round lengths to the nearest thousandth and angle measures to the nearest degree. 56.) Find FG. 57.) Find

58.) Find XZ. 59.) Find

m∠Q. m∠T.

Review Chapter 9 60.) Find the area of the parallelogram.

61.) Find the length of a rectangle in which and .

62.) Find the perimeter of a rectangle in which the width is 21 cm and the

63.) Find the area of a trapezoid in which

64.) Find the base of the triangle, in which

65.) Find of the trapezoid, in which

w = 3 in A = 6x2 + 24x − 6( ) in2

A = 79.8x2 − 42( ) cm2.

b1 = 8 in; b2 = 5 in; and h = 6.2 in.

h = 5x( )cm and A = 15x2( ) cm2.

b2 b1 = 23 mm; h = 11 mm; A = 231 mm2.

66.) Find the area of the rhombus, in which Write in simplest form. 67.) Find the area of the kite by first solving for x and y.

68.) Find the height of a parallelogram if the sides are (11.5x)mm and (20x)mm, and the area is

69.) Find the perimeter of a rectangle in which w=12 cm and

70.) Find the area of in terms of if the diameter is 6 in.

d1 = 8x + 7( ) cm; d2 = 14x − 6( ) cm.

182x2( )mm2.

A = 32x2( ) cm2.

⊙K π,

71.) Find the circumference of if the area is

72.) Find the area of a regular heptagon with side length 2 ft. 73.) Find the area of a regular nonagon with side length 8 cm. 74.) Find the area of a regular octagon with an apothem length of 4 in. 75.) Find the area of the circle not including the inscribed trapezoid.

⊙M 25x2π( ) ft2.

76.) The base and height of a rectangle are both doubled. What effect does this have on the perimeter? What about the area?

77.) The radius of a circle is multiplied by What effect does this have on the circumference and the area?

78.) Find the probability that a point chosen randomly inside the rectangle is in the triangle. The base of the

triangle is 6 in. 79.) Use the spinner below to find the probability of the pointer landing in the following areas.

a.) b.)

Chapter 10 Review For each problem, draw a diagram. Leave your answer as a fraction, simplified radical, and in terms of 80.) What is the length of the diagonal of a cube with a side length of 12 cm?

15.

110° 70° or 85°

π.

81.) What is the height of a rectangular prism with a 20 cm by 12 cm base and a 30 cm diagonal? 82.) Find the lateral area and surface area of a right triangular prism with height 40 cm and base edges of 16

cm. 83.) Find the lateral area and surface area of a cylinder with a diameter of 18in and a height of 10in,

84.) Find the lateral area and surface area of a cylinder with a circumference of and a height equal to half the radius.

85.) Find the lateral area and surface area of a hexagonal prism with height 30 in and base edge length 12 in. 86.) Find the lateral area and surface area of a regular square pyramid with base edge length 14 cm and a

slant height of 26 cm. 87.) Find the lateral area and surface area of a right cone with radius 12 cm and a height of 5 cm.

24π cm

88.) Find the lateral area of a right cone with radius 8 m and a height of 15 m. 89.) Find the volume of a right regular hexagonal prism with height of 12 in and base edge length of 9 in.

90.) Find the volume of a cylinder with base area and a height equal to twice the radius. 91.) Find the volume of a square pyramid with a base edge length 9 cm and a height of 19 cm.

121π cm2

92.) Find the volume of a sphere if the diameter of the great circle is 24 in. 93.) Find the diameter of a sphere with volume cm3. 94.) Find the volume of a hemisphere with radius 15 m. 95.) Find the surface area of a sphere with a diameter of 76 cm.

36,000π

96.) Find the volume of a sphere with a surface area of 324

97.) Find the surface area of a sphere with a great circle that has an area of 49 Chapter 11 Review Any measurements not labeled are in meters. Leave answers in simplest radical form, in fractions, and in terms of unless otherwise specified.

98.) are tangent lines. Find FG.

99.) Find m .

π.

π mi2.

π,

FE and FG DCA!

100.) 101.) 102.) Find PL to the nearest thousandth. 103.) Find the area of sector LKM.

104.) Find the area of sector AKL.

AB ≅ CD. AB = 9n − 11( )cm and CD = 7n + 11( )cm. Find CD.

⊙C ≅ ⊙J, DG = 14x − 26, MN = 5x + 1, and m∠GCD = m∠NJM. Find NM.

⊙T ≅ ⊙U, and AC = 47.2.

105.) Find the area of segment AKL.

106.) Find

107.) Find each measure if a.) b.)

c.) d.) e.)

f.)

108.) Find the

m∠LAK when m∠LAK = 5x − 7( )° and m∠LDK = 3x( )°.

m∠ACF = 112° and mAB! = 145°.

m!DAB

m!ECA

mBC!

m!DAC

m!BAC

mAC!

m∠AED, if mBC! = 113° and mAD! = 139°.

109.) Find the value of x.

110.) Find the value of x.

111.) Solve for .

112.) Solve for x.

113.) Solve for x.

114.) Solve for x.

mYZ!

11

Chapter 0 Review Solve the following problems by writing an expression, showing all work, and writing your answer in a complete sentence in the specified notation.

115.) If sound travels miles in one hour. How many miles will it travel in 1 minute? Write your answer in scientific notation.

116.) A speck of dust in an electron microscope is millimeters wide. The image is times larger than the actual size. How many millimeters wide is the actual speck of dust? Write your answer in standard notation.

117.) The state of Connecticut covers square miles. The Indian Ocean covers about square miles. How many times bigger than Connecticut is the Indian Ocean? Write your answer in scientific notation.

118.) The population of the United States is and the population of the world is . How many times larger is the population of the world than the US? Write your answer in scientific notation.

7.67 × 102

0.15× 10−3 5× 103

6 × 103 1.2× 107

3.5× 108 7 × 109

Convert the following fractions, decimals, and percents into the values that are not already given. For example, if a fraction is given, you must convert into the decimal and percent equivalencies. All fractions must be simplified.

119.)

120.) 121.)

122.)

123.)

124.)

125.)

126.)

127.)

128.)

1920

0.48

8.2%

3140

8.5%

0.951

3800

175000

7.52

2.839

Simplify. Leave your answer in exponential notation with positive exponents and if possible one base. Show all work.

129.)

130.)

131.)

132.)

133.)

134.)

25−15

25−8

78( ) 498( )

−6( )−7⎛⎝⎜⎞⎠⎟−6

2162 ⋅615( )3

−223

⎛⎝⎜

⎞⎠⎟

−6⎛

⎝⎜⎜

⎞

⎠⎟⎟

12

81

312

Proof Review – Write a two-column proof for each.

135.) Given: Prove:

EB ⊥ AC; BH ⊥ AE; CJ⊥ AEΔABH~ ΔDCB

136.) Given:

Prove:

LP !MN

LJJN

= PJJM

137.) Given:

Prove:

VR !WS; WS bisects "RWT

RWWT

= RSST

138.) Given:

Prove:

RU bisects !SRT; VU "RTSVVR

= SRRT

139.) Given:

Prove:

JF bisects !EFG; EH " FG; EF " JGEKKF

= GJJF

140.) Given:

Prove:

!C ≅ !BDA

ACDA

= ADBA

141.)

142.)

143.)

144.) Given: RSTU is a parallelogram Prove:

ΔRSU ≅ ΔTUS

145.) Draw the diagram. Given: ABCD is a rhombus. E is the midpoint of ; F is the midpoint of

Prove: AEFD is a parallelogram

AB CD

146.) Given: ABCD is a rhombus and Prove:

BE = DFΔABE ≅ ΔCDF