Download Geometry Chapter 4 Test Review Name: Congruent Triangles Date

Geometry Chapter 4 Test Review
Congruent Triangles
Name:
Date:
Period:
1. Classify ∆𝐸𝐹𝐺.
F
8
E
9
10
G
2. Name an acute triangle.
B
35 55
A
30
115 65
D
60
C
3. How many acute angles can an isosceles triangle have? Explain.
4. Draw and identify a triangle with
a) Angle measures of 50, 65 and 65
b) Angle measures of 80, 75 and 45
5. How many obtuse angles can a triangle have? Explain.
6. Find the value of x.
96°
x
127°
Geometry Chapter 4 Test Review
Congruent Triangles
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7. Find the value of x.
57°
116°
[A] 116
[B] 237
x°
[C] 57
[D] 59
8. Find the value of x.

x
9. Find the measure of the interior angles to the nearest tenth. (Drawing is not to scale.)
3𝑥 + 2 °
4𝑥 + 1 °
2𝑥 + 1 °
10. Find the measure of ∡𝐴 below.
Geometry Chapter 4 Test Review
Congruent Triangles
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11. The measure of ∡𝐵 is _____.
[A] 89°
[B] 99°
[C] 101°
[D] 79°
12. If ∠𝑃 ≅ ∡𝑄 and 𝑚∡𝑄 = 2𝑥 + 4 and 𝑚∡𝑃 = 34, what is the value of x?.
13. If ∆𝑅𝑃𝑄 ≅ ∆𝐽𝐾𝐿, then 𝐿𝐽 ≅_____ . Draw a diagram to support your claim.
14. The two triangle-shaped gardens are congruent. Find the missing side lengths and angle
measures.
d=
33°
h
e=
e
10.1
8.5
f=
g=
g
57°
f
5.5
d
h=
15. Sketch the following, if possible. If not possible, state why.
A. Right isosceles triangle
B. Acute triangle with two obtuse angles
C. A triangle with an exterior angle of 45
D. A triangle with two acute angles and one obtuse angle
16. In the diagram, ∡𝐵 ≅ ∡𝐸 and ∡𝐶 ≅ ∡𝐹. Find the value of x.
B
A
𝑥 + 50 ° 35° C
D
75°
F
E
Geometry Chapter 4 Test Review
Congruent Triangles
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17. Refer to the figure below. Which of the following statements is true?
E
G
D
F
DEF is equilateral 𝐷𝐺 ≅ 𝐹𝐺
[A] ∆𝐷𝐺𝐸 ≅ ∆𝐹𝐺𝐸 by SSS
[B] ∆𝐷𝐼𝐺 ≅ ∆𝐹𝐼𝐺 by SAS
[C] ∆𝐷𝐹𝐺 ≅ ∆𝐺𝐸𝐷 by SSS
[D] There are no congruent triangles.
18. State two postulates or theorems that can be used to conclude that ∆𝐴𝑂𝐵 ≅ ∆𝐶𝑂𝐷.
19. Refer to the figure shown. Which of the following statements is true?
U
V
W
T
TV  WV
UV  XV
X
[A] ∆𝑇𝑈𝑉 ≅ ∆𝑉𝑊𝑋 by SAS
[B] ∆𝑇𝑈𝑉 ≅ ∆𝑊𝑋𝑉 by SAS
[C] ∆𝑇𝑈𝑉 ≅ ∆𝑋𝑊𝑉 by ASA
[D] ∆𝑇𝑈𝑉 ≅ ∆𝑊𝑋𝑉 by ASA
Geometry Chapter 4 Test Review
Congruent Triangles
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20. Which postulate or theorem can be used to determine the measure of 𝑅𝑇?
21. Given:∡𝐵 ≅ ∡𝐸 and ∡𝐶 ≅ ∡𝐹. What other piece of information is needed to show
∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹 by ASA Congruence Postulate?
[A] ∡𝐴 ≅ ∡𝐷
[B] 𝐵𝐶 ≅ 𝐸𝐹
[C] ∡𝐵 = ∡𝐹
[D] 𝐸𝐹 ≅ 𝐹𝐸
22. What is the measure of each base angle of an isosceles triangle if its vertex angle measures
40 degrees and its 2 congruent sides measure 23 units?
40°
23
23
23. ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹. Also 𝐴𝐵 ≅ 𝐸𝐹 . What type of triangle is ∆𝐴𝐵𝐶? Explain.
24. In ∆𝐴𝐵𝐶, 𝐴𝐵 ≅ 𝐵𝐶 , which term does NOT describe the triangle?
[A] Obtuse
[B] Isosceles
[C] Equilateral
25. Find the values of x and y.
x
112°
y
[D] Acute
Geometry Chapter 4 Test Review
Congruent Triangles
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26. Use information in the figure below to find 𝑚∡𝐷.
E
101°
D
F
27. ∆𝐴𝐵𝐷 ≅ ∆𝐶𝐵𝐷. Name the theorem or postulate that justifies the congruence.
A
B
D
C
28. Given: 𝐸𝐷 ⊥ 𝐸𝐶 ; 𝐵𝐷 ⊥ 𝐵𝐶 ; 𝐸𝐷 ≅ 𝐵𝐶
Based on this information, Prove:∆𝐶𝐸𝐷 ≅ ∆𝐷𝐵𝐶
A
E
B
D
C
29. Refer to the figure below.
A. Is there enough information to know whether ∡𝐹𝐸𝐺 is acute, obtuse, or a
right angle? Explain.
B. If 𝑚∡𝐹 is less than 45°, what type of angle is ∡𝐹𝐸𝐺? Explain.
30. Find the measure of ∡𝐵.
49°
128°
B
Geometry Chapter 4 Test Review
Congruent Triangles
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31. Given: 𝐵𝐶 ≅ 𝐷𝐴, ∡1 ≅ ∡2, and 𝐶𝐹 ≅ 𝐴𝐹
Prove: ∆𝐶𝐸𝐹 ≅ ∆𝐴𝐸𝐹
B
D
2
1
E
C
A
F
32.
Period:
Geometry Chapter 4 Test Review
Congruent Triangles
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[1] Scalene
[2] BDC
[3] It can have two acute angles if it is a
right isosceles or an obtuse isosceles
triangle; otherwise it will have 3 acute
angles.
[4] a. Acute Isosceles
50° 65°
65°
b. Acute Scalene
75°
80°
45°
[5] One, If you have more than one obtuse
angle, the sum of the three angles would be
larger than 180.
[6] 31°
[7] [D]
[8] 24°
[9] 40.1, 60.7, 79.2
[10] 131°
[11] [C]
[12] 15
[13] QR
[14] d = 5.5, e = 33, f = 90, g = 57,
h = 10.1
Period:
[15] A, C and D are possible. Sketches vary.
B is not possible.
[16] 25
[17] [A]
[18] SAS and SSS Congruence Postulates
[19] [B]
[20] AAS
[21] [B]
[22] 70°
[23] Isosceles. ABC  DEF , so
BC  EF . Then, since AB  EF ,
AB  BC by the Transitive Property of
Congruence. Therefore, ABC is isosceles.
[24] [A]
[25] 𝑥 = 44°, 𝑦 = 68°
[26] 39.5°
[27] AAS
[28] Look below for proof.
[29] A. No. There is no information about
the measures of angles F and G.
B. Obtuse. If F is less than 45°,
FEH is greater than 45°. Since the 2
triangles are congruent by SAS, GEH is
greater than 45°. Therefore, FEG is
greater than 90°, which means it is obtuse.
[30] 79°
[28]
1. ED  EC
2.  CED is a rt 
3. BD  BC
4.  DBC is a rt 
1. Given
2. If 2 segm ents are , they form rt s.
3. Given
4. If 2 segm ents are , they form rt s.
5. ED  BC
6. DC  CD
7.  CED   DBC
5. Given
6. Reflexive
7. HL Congru ence Theorem
Geometry Chapter 4 Test Review
Congruent Triangles
31. . Statements
1. 𝐵𝐶 ≅ 𝐷𝐴
32.
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Reasons
1. Given
2. ∡1 ≅ ∡2
2. Given
3. ∡𝐵𝐸𝐶 ≅ ∡𝐷𝐸𝐴
3. Vertical Angles Theorem
4. ∆𝐵𝐸𝐶 ≅ ∆𝐷𝐸𝐴
4. AAS
5. 𝐸𝐶 ≅ 𝐸𝐴
5. CPCTC
6. 𝐶𝐹 ≅ 𝐴𝐹
6. Given
7. 𝐸𝐹 ≅ 𝐸𝐹
7. Reflexive Property
8. ∆𝐶𝐸𝐹 ≅ ∆𝐴𝐸𝐹
8. SSS