Honors Geometry 5. Homework Answers for Section 9.7 The perimeter of a square is 44. Find the length of a diagonal.
11
11
Using the isosceles right triangle lengths,
the diagonal is 11 2
11
11 2
11
6. Find the length of the diagonal of the rectangle.
16 (2x)
8 (x)
8
3 (x
30°
3)
7. Find the altitude of an equilateral triangle if a side is 6 mm long.
C
6
6
3 3
60°
A
Baroody 3
3
B
Page 1 of 4 Honors Geometry 8. Homework Answers for Section 9.7 Given:
AC ⊥ BC, CD ⊥ AB,
m∠B = 30°, BC = 8 3
Find:
CD
A
D
12
4 3
30°
C
8 3
9. Given:
TRWX is a kite (TR ≅ WR and TX ≅ XW)
RY = 5, TW = 10, YX = 12
Find:
a. TR
b. WX
B
W
13
5
10 R
5 Y
12
X
5
5 2
T
12. a. Find the coordinates of B
(1,
3)
B
b. Find the slope of OB
m=
3 -0
=
1-0
2
3
AB
(In trigonometry, this ratio is called
OA
the tangent of ∠BOA)
c. Find
AB
3
=
=
OA
1
Baroody 3
60°
O (0, 0)
1
A (1, 0)
3
Page 2 of 4 Honors Geometry 15. Homework Answers for Section 9.7 Find the perimeter of the isosceles trapezoid EFGH (Hint: drop altitudes of the trapezoid from E and H).
E
6
H
10
P = 6 + 10 + 6 + 16 = 38
3 3
60°
F
3
10
3
G
16
16. Given:
PK is an altitude of isosceles trapezoid JMOP.
PK = 6, PO = 8, m∠J = 45°
Find:
The perimeter of JMOP
P
O
8
6 2
6 2
6
P = 6 2 + 8 + 6 2 + 6 + 8 + 6 = 28 + 12 2
45°
J
6
8
K
6
M
17. Using the figure, find
T
a. VS
9
S
30°
b. ST
c. VT
6 3
d. The ratio of the perimeter of
the perimeter of VRT
Baroody P
VSR
P
VRT
=
9+3 3
=
18 + 6 3
3 3
R
3
60°
6
VSR to
9+3 3
2(9 + 3 3 )
V
=
1
2
Page 3 of 4 Honors Geometry 18. Homework Answers for Section 9.7 One of the angles of a rhombus has a measure of 120°. If the perimeter of the rhombus is 24, find the length
of each diagonal.
6
B
C
60°
60°
3
6
6
E
A
Since BE =
3 3
Since CE =
1
BD, BD = 2(3) = 6
2
1
2
CA, CA = 2(3 3 ) = 6 3
D
6
22. Find the length of the altitude to the base of the isosceles triangle shown.
60° 60°
3 3
9
6 3
9
24. Find x and y.
C
9
2
3
3
Baroody 3
30°
30°
30°
B
2
3 3
A
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