Unit 8 Quiz Review Answers
Find the geometric mean(s) between each pair of numbers.
1. 10 & 8
2. 15 & 5
3. 50 & 40
10 = x
15 = x
50 = x
x
8
x
5
x
40
x2 = 80
x2 = 75
x2 = 2000
x = ±4 sqrt(5)
x = ±5 sqrt(3)
x = ±40 sqrt(5)
Find the measure of the angle’s supplement:
4. the ratio of an angle to its complement 5. the ratio of an angle’s complement
is 2:3.
to its supplement is2:5.
2x + 3x = 90
5x = 90
x = 18 2(18) = 36 (angle)
supplement is 180 – 36 = 144º
90 – x = 2
180 – x
5
450 – 5x = 360 – 2x
90 = 3x
30 = x; supplement is 150 º
Give the similarity statement (IF the Δs are ~). [Δ _____~ Δ______ by _____]
A
6. J
M
7.
J
4
6
W
M
R
ΔJAW ~ ΔAMR by AA
W
A3
J
8.
12
15
2
R
2 = 3
4
6
A
W
8
10
R
M
ΔJAM ~ ΔRAW by SAS~
12 = 15
20
25
ΔJAW ~ ΔJRM by SAS~
J
W
9.
10.
10
30
J
M
7
10.5
W
8
A
24
10
G
R
M
A
8
30 = 24
10
8
Although the ratios are equal, the Δ are not
similar, b/c the congruent < is in the wrong
place (angle-side-side)
15
R
7 = 10
10.5 15
105 = 105
8 = 10 G
11.5 15
120 = 115
NO!
11.5
A-Geometry: Similarity
Set up a proportion and solve:
A
1. A
2.
x
E
10
8
x
E
B
B
8
5
13
=
5
C
D
C
8 = x
11
x+4
x
10
13x = 50
x = 50/13
A
A
4.
D
5
x
5
D
11x = 8x + 32
3x = 32
x = 10 2/3
4
3.
3
4
x
E
6
B
3
B
C
4
5
=
5
4+x
4x + 16 = 25
4x = 9
x = 2.25
D
C
x
8
=
5
x+6
x2 + 6x = 40
x2 + 6x – 40 = 0
(x + 10)(x – 4) = 0
x = -10 x = 4