STUDY GUIDE for FINALS in GEOMETRY
The triangles are similar.
2)
1)
3)
6)
5)
4)
7)
Find the perimeter of the given triangle. Round your answer to the nearest tenth if necessary.
9)
8)
11) ΔBCE, if ΔADF ~ ΔBCE, given AD = 27, DF = 24
AF = 21, and BC = 18.
10)
A
B
C
E
F
12) Find the measure of the altitude.
13) Find the measure of the altitude.
A
8
D
15
C
B
FIND x.
16) 15) 14) x
Review the SPECIAL RIGHT TRIANGLES
17) =
18) =
D
Find each measure using the given measures of the triangle. Round angle measures to the nearest degree and side measures to the nearest tenth.
19) 20) 21) 22) 23) 24) 25) 26) Find the measure of each interior angle of a regular polygon. Round to the nearest tenth if necessary. 28) dodecagon 27) pentagon Find the measure of each exterior angle of a regular polygon. Round to the nearest tenth if necessary. 29) nonagon
30) decagon 31) If AG = ­4k + 24 and DG = 9k + 102, find BD. 32) If ADB = 2y + 40 and CDB = ­3y + 51, find CBD.
33) In rhombus YZAB, if YZ = 12, find AB. 34) In rhombus TUVW, if m TUW = 34, find m UVT. Find the missing measure for the given trapezoid.
35) 37) 36) 38) For trapezoid ABCD, E and F are midpoints
of the legs. Let GH be the median of ABFE.
Find GH. 39) Let GH be the median of RSBA. Find GH. 40) Let JK be the median of ABTQ. Find JK. 41) 42) Find x. Assume that segments that appear to be tangent are tangent.
43) 44) Find the measure of the numbered angle.
45) 47) 46) 49) 48) Find the value of x. Assume that segments that appear to be tangent are tangent.
50) 53) 51) 54) 52) 55) 57) 56) 58) 60) 59) 61) Write an equation for a circle with center at (­10, 9) and diameter = 22
62) Write an equation for a circle with center at (­6, 10) and diameter = 6
63) Write an equation for a circle with a diameter that has endpoints at (10, ­9) and (­6, ­7).
64) Write an equation for a circle with a diameter that has endpoints at (­10, 1) and (­8, 5).
Find the perimeter and area of the parallelogram. Round to the nearest tenth if necessary.
65) 66) 67) 68) Find the area of each figure. Round to the nearest tenth if necessary.
71) 70) 69) 72) 73) 74) 75) Find the area of a regular pentagon with apothem length of 5.5 meters. Round to the nearest tenth if
necessary. Find the area of each figure. Round to the nearest tenth if necessary.
76) 77) 16
78) 79) 80) 81) 82) 84) 83) Find the area of the indicated sector(s). Then find the probability of spinning the color indicated if the diameter of the spinner is 20.
85) brown 86) blue 87) pink Find the area of the shaded region. Round answers to the nearest tenth. Assume all inscribed polygons are regular.
89) 88) 90) ANSWERS
1) x = 5; AB = 14 units; BC = 8 units 2) x = 3; EB = 15 units; ED = 42 units 3) x = 1.5; AB = 3 units
4) x = 8; AS = 8 units
5) x = 4; BD = 8 units; CE = 36 units 6) x = 21
7) Yes because RQ RS
=
QP ST
8) Perimeter of ΔBCD = 25.5 units
9) Perimeter of ΔDEF = 12.75 units
10) Perimeter of ΔADF = 63 units
11) Perimeter of ΔBCE = 48 units
12) BD = 2√30 or BD ≈ 10.95
13) CD = 2√3 or CD ≈ 3.46
14) x = 13 ft
15) x = 8 units
16) x = 4√3 0r x ≈ 6.93
17) A ≈ 54.8
18) B ≈ 39.1
19) k ≈ 21
20) K ≈ 57
21) b ≈ 6.7
22) F ≈ 40
23) x ≈ 8.5
24) x ≈ 29.1
25) x ≈ 22.6
26) x ≈ 28.2
27) each interior angle = 108
28) each interior angle = 150
29) each exterior angle = 40
30) each exterior angle = 36
31) BD = 96 units
32) m CBD = 42
33) AB = 12 units
34) m UVT = 56
35) AB = 23 36) ML = 40
37) ML = 28
38) GH = 6
39) GH = 62
40) JK = 78
41) m 1 = 20
42) m BCE = 111
43) x = 8
44) x = 6
45) m 6 = 125
46) m 9 = 90
47) x = 40
48) x = 43
49) x = 65
50) x = 9
51) x = 3.2
52) x = 2√14 or x ≈ 7.5
53) x = 3
54) x = 4
55) x = 5
56) x = 10
57) x = 2.275
58) x ≈ 9.6 59) x = 6
60) x ≈ 2.7
61) (x + 10)2 + (y ­ 9)2 = 121
62) (x + 6)2 + (y ­ 10)2 = 9
63) (x ­ 2)2 + (y + 8)2 = 65
64) (x + 9)2 + (y ­ 3)2 = 5
65) P = 70 in ; A = 259.8 in2
66) P = 74 ft ; A = 178.2 ft2
67) P = 49 m ; A = 113.5 m2
68) P = 50 in. ; A = 106.1 in2
69) A = 11.5 yd2
70) A = 11.8 yd2
71) A = 192 mm2
72) A = 146.5 cm2
73) A = 442 in2
74) A = 374 yd2
75) A = 109.9 m2
76) A = 713.1 units2
77) A = 80 cm2
78) A = 217 mm2
79) A = 612.5 units2
80) A = 100 ft2
81) A = 76 m2
82) A = 33.3 m2
83) A = 29 units2
84) A = 20.5 units2
85) A(brown) ≈ 174.5 units2
P (brown) ≈ 0.56
86) A(blue) ≈ 120.4 units2
P (blue) ≈ 0.38
87) A(pink) ≈ 115.2 units2
P (pink) ≈ 0.37
88) A(shaded region) = 9.2 units2
89) A(shaded region) = 29.3 units2
90) A(shaded region) = 29.3 units2