Honors Geometry Homework Answers for Section 5.5 4.
Given:
Prove:
ABCD is a parallelogram
AE ≅ CF
D
C
F
DE ≅ BF
E
A
B
Statements
Reasons
1. ABCD is a parallelogram
S 2. AD ≅ BC
1. Given
2. Opposite sides of a parallelogram are ≅
S 3. AE ≅ CF
4. AD BC
A 5. ∠DAE ≅ ∠BCF
6. AED ≅ CFB
3.
4.
5.
6.
7. DE ≅ BF
Given
Opposite sides of a parallelogram are
PAI
SAS (2, 5, 3)
7. CPCTC
5.
WSTV is a parallelogram.
Find the perimeter of WSTV
W
x+9
V
x+5
2x + 1
x + 5 = 2x + 1
⇒x = 4
⇒ PWSTV = 2(x + 5) + 2(x + 9) = 18 + 26 = 44
S
Baroody T
Page 1 of 5 Honors Geometry Homework Answers for Section 5.5 6.
ABCD is a parallelogram.
Find m∠D and m∠C
D
(3x - 4) + x = 180
C
(3x - 4)°
⇒ 4x = 184
⇒ m∠A = x = 46°
(x)°
⇒ m∠D = (3x - 4) = 3(46) - 4 = 134°
A
B
7.
EFGH is an isosceles trapezoid with legs HE and GF. EJ = x + 5,
JG = 2x - 1, and HF = 13.
Find EJ, JG, and HJ
Since EG = HF,
H
(x + 5) + (2x - 1) = 13
G
3x = 9
2x - 1
J
x=3
x+5
∴ EJ = x + 5 = 8
JG = 2x - 1 = 5
F
E
HJ = JG = 5
11.
Find KT
I
(5x - 10)°
K
6x
P
T
∠IPT = 90 = 5x - 10
⇒ 5x = 100
⇒ x = 20
∴ KT = 2(KP) = 2(120) = 240
E
Baroody Page 2 of 5 Honors Geometry Baroody Homework Answers for Section 5.5 Page 3 of 5 Honors Geometry Homework Answers for Section 5.5 12.
RECT is a rectangle.
Find ET to the nearest tenth.
R
43x = 214x - 742
E
⇒ 171x = 742
43x
A
⇒ x ≈ 4.339
214x - 742
∴ ET = RC = 257x - 742 ≈ 373.2
C
T
17.
Given:
RVTS is an isos.
trapezoid with legs
VR & TS
V
T
A
Prove:
ARS is isosceles
S
R
Statements
1. RVTS is an isos. trapezoid with
legs VR & TS
Reasons
1. Given
S 2. VR ≅ TS
2. Definition of Legs of Isos Trapezoid
S 3. VS ≅ TR
S 4. RS ≅ RS
5. VRS ≅ TSR
6. ∠TRS ≅ ∠VSR
7. AR ≅ AS
8. ARS is isosceles
3.
4.
5.
6.
7.
8.
Baroody Diagonals of an isos trapezoid are ≅
Reflexive Property
SSS (2, 3, 4)
CPCTC
Converse of ITT
Definition of Isos.
Page 4 of 5 Honors Geometry Homework Answers for Section 5.5 19.
KMOP is a parallelogram.
Find m∠K
M
(x + 3y) + (x - 4) = 180
⇒ 2x + 3y = 184
(x + 3y) = (4y - 8)
⇒x=y-8
O
(x + 3y)°
2(y - 8) + 3y = 184
(x - 4)°
⇒ 5y = 200
⇒ y = 40
(4y - 8)°
K
⇒ x = 40 - 8 = 32
P
∴ m∠K = m∠O = 32 - 4 = 28°
20.
ABCD is an isosceles trapezoid with upper base AD. BD = y + 4.
Find AC
A
D
(x + 5) + (y - 3) = y + 4
E
x+5
⇒x=2
AC = AE + BE
x+7
y-3
= 7 + 9 = 16
C
B
29.
m
m
n
a. Solve for a in terms of x and y
y°
a = (180 - y) + x = x - y + 180
(180 - y)° y°
x°
b. If a > 90, what must be true of y - x?
n
Baroody x°
If a > 90 ⇒ x - y + 180 > 90 ⇒ y - x < 90
Page 5 of 5