Preparing for the Regents Examination Geometry, AK

12-8 Proportions in a
Right Triangle
(pages 323–324)
1 (1) 10
2 (3) √ 21
3 (3) 4
4 (1) √ 77
5 a False b True c False
d False e True f True
g True
6 2 √ 15
7 5
8 6
9 √ 55
h False
10 x 2 √ 5 , y 4 √ 5 , z 4
11 x 2 √ 5 , y 4 √ 5 , z 8
12 x 3 √ 6 , y 6 √ 3 , z 6
13 x 4 √ 3 , y 8 √ 3 , z 12
14 x 20, y 8 √ 6 , z 40 √ 6
15 x 9, y 6.75, z 18.75
16 x 4 √ 5 , y 10
17 x 3 √ 10 , y 3 √ 6 , z 3 √ 15
18 x 12, y 4 √ 5 , z 6 √ 5
19 x 9, y 6, z 6 √ 3
20 x 25, y 17.5, z 29.2
21 x 2.4, y 3.2, z 1.8
22 a x 21 b (10) 2 23 13
x(x 21) c 4
24 a LR 2 √ 26 1, LM 4 √ 26
b 9 and 10
12-9 Pythagorean Theorem
and Special Triangles
(pages 327–329)
1 (2) 10 √ 2
2 (3) 25 feet
3 (1) √ 13
4 (1) 50 miles
5 (4) √ 41
6 (1) 24 feet
7 (2) 13
8 (4) {10, 24, 26}
9 14
10 b, c, d, e, f, g
11 a 3 √ 2 b √ 3 c
d 9 e 5 _
12
f
√
5
√
14
12 6
13 8
14 240 cm 2
15 32 in.
16 x 10 √ 5 , 2x 20 √ 5
17 24
18 5
19 19.2 in.
20 Perimeter is 56. Area is 192.
21 3
22 10
23 3 √ 3
24 BD 2 a 2 b 2
BD 2 d 2 c 2
a 2 b 2 d 2 c 2
a 2 d 2 b 2 c 2
25 AB 2 BC 2 AC 2
AC 2 AD 2 CD 2
AB 2 BC 2 AD 2 CD 2
Special Triangles
(pages 332–334)
1 (1) 6 √ 2 ft and 6 √ 2 ft
2 (3) 1 : √ 3 : 2
3 (4) 6 √ 2
4 (1) 1
5 (2) 6 √ 3
6 (1) 30
7 (3) 3.75
8 (2) 2 √ 6
9 (3) 60
10 a BC 7, AC 7 √ 3
b BC 2.5, AC 2.5 √ 3
c BC 3 √ 3 , AC 9
d AC 9 √ 3 , AB 18
e AC 12, AB 8 √ 3
f BC 7, AB 14
g BC 2.75 √ 3 , AC 8.25
h BC 4 √ 3 , AB 8 √ 3
11 a AC 4, AB 4 √ 2
b BC 10, AB 10 √ 2
c AC 8, BC 8
d AC 1.5, BC 1.5
e AC 6 √ 2 , BC 6 √ 2
f BC 3 √ 2 , AB 6
g BC 10 √ 2 , AB 20
h AC 7.5 √ 2 , BC 7.5 √ 2
i BC 4 √ 3 , AB 4 √ 6
j AC 4 √ 6 , BC 4 √ 6
12-9 Pythagorean Theorem and Special Triangles 77