Download Chapter 4 Review no 4.7

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Geometry Chapter 4 Test Review
Classify each triangle as acute, obtuse or right.
1.
2.
3.
30°
50°
120°
25°
65°
35°
60°
65°
Classify each triangle as scalene, isosceles or equilateral.
4.
5.
x
6.
23
12
x
15
x
7. Find x and the measure of each side of equilateral triangle FGH if 𝐹𝐺 = 𝑥 + 5, 𝐺𝐻 = 3𝑥 − 9 , and 𝐹𝐻 = 2𝑥 − 2.
8. Triangle LMN is an isosceles triangle with ̅̅̅̅
𝐿𝑀 ≅ ̅̅̅̅
𝐿𝑁. Find b, and the measures of the sides if ̅̅̅̅
𝐿𝑀 = 3𝑏 − 2 , 𝑀𝑁 =
5𝑏 − 2, and 𝐿𝑁 = 2𝑏 + 1.
9. Find the missing angles.
85°
55°
1
2
40°
3
10. Find the measures of the numbered angles
3
2
1
55°
150°
70°
11. Identify the congruent triangles in each figure.
a.
b.
12. Name the congruent angles and sides for the following pair of congruent triangles.
∆𝑅𝑆𝑇 ≅ ∆𝐿𝑀𝑁
13. Determine whether ∆𝑃𝑄𝑅 ≅ ∆𝑆𝑇𝑈 given the coordinates of the vertices. EXPLAIN
P(0, 3), Q(0, -1), R(-2, -1), S(1, 2), T(1, -2), U(-1, -2)
14. Determine which postulate can be used to prove the triangles are congruent. If it is not possible to determine they are
congruent, write “not possible”.
a.
b.
c.
15. ∆𝐴𝑅𝑀, ∆𝑀𝐴𝑋, ∆𝑋𝐹𝑀 are all isosceles triangles.
What is m∠𝐴𝑀𝑋 ?
X
F
72º
What is m∠𝑅𝐴𝑋 ?
M
38º
A
If m∠𝐹𝑋𝐴=96, what is m∠𝐹𝑀𝑅 ?
R
̅̅̅̅ bisects ̅̅̅̅
16. Triangle RSU is an equilateral triangle. 𝑅𝑇
𝑈𝑆. Find x and y.
R
(y - 2)°
8x + 1
U
T
5x
S
A
̅̅̅̅ bisects 𝐶𝐷
̅̅̅̅ ; ∠𝐴 ≅ ∠𝐵
18. Given: 𝐴𝐵
D
X
Prove: ̅̅̅̅
𝐴𝑋 ≅ ̅̅̅̅
𝐵𝑋
C
Statements
1. ̅̅̅̅
𝐴𝐵 bisects ̅̅̅̅
𝐶𝐷; ∠𝐴 ≅ ∠𝐵
Reasons
̅̅̅̅ ≅ 𝑋𝐷
̅̅̅̅
2. 𝐶𝑋
2.
3. ∠𝐴𝑋𝐶 ≅ ∠𝐷𝑋𝐵
3.
4. ∆𝐴𝑋𝐶 ≅ ∆𝐷𝑋𝐵
4
5. ̅̅̅̅
𝐴𝑋 ≅ ̅̅̅̅
𝐵𝑋
5.
B
1.
̅̅̅̅ ≅ 𝑌𝑊
̅̅̅̅̅ ; ∠𝑆 ≅ ∠𝑊
19. Given: 𝑆𝑌
Statements
Prove: ∆𝑆𝑌𝑇 ≅ ∆𝑊𝑉𝑌
V
S
Y
T
W
Reasons
̅̅̅̅ ∥ 𝑀𝐿
̅̅̅̅ ; 𝐹𝐿
̅̅̅̅ ∥ 𝑀𝑃
̅̅̅̅̅
20. Given: 𝐹𝑃
Prove: ̅̅̅
𝐹𝐿̅ ≅ ̅̅̅̅̅
𝑀𝑃
F
Statements
Reasons
Statements
Reasons
L
1
3
4
2
P
M
̅̅̅̅ ≅ 𝐵𝐶
̅̅̅̅ ;
21. Given: 𝐴𝐵
D is the midpoint of ̅̅̅̅
𝐴𝐶
Prove: ∆𝐴𝐵𝐷 ≅ ∆𝐶𝐵𝐷
B
A
D
C
Write a two column proof for each:
23. Given: 8𝑥 − 5 = 2𝑥 + 1
Prove: 𝑥 = 1
24. Given: 5(𝑛 − 3) = 4(2𝑛 − 7) − 14
Prove: 𝑛 = 9
𝑥
25. Given: 4 = 5 − 16
Prove: 𝑥 = 100