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Transcript
Geometry Chapter 4 Test Review
Congruent Triangles
Name:
Date:
Period:
1. Classify βˆ†πΈπΉπΊ.
F
8
E
9
10
G
2. Name an acute triangle.
B
35ο‚° 55ο‚°
A
30ο‚°
115ο‚° 65ο‚°
D
60ο‚°
C
3. How many acute angles can an isosceles triangle have? Explain.
4. Draw and identify a triangle with
a) Angle measures of 50ο‚°, 65ο‚° and 65ο‚°
b) Angle measures of 80ο‚°, 75ο‚° and 45ο‚°
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
Name:
Date:
Period:
7. Find the value of x.
57°
116°
[A] 116
[B] 237
x°
[C] 57
[D] 59
8. Find the value of x.
ο€Άο€Άο‚°
x
9. Find the measure of the interior angles to the nearest tenth. (Drawing is not to scale.)
3π‘₯ + 2 °
4π‘₯ + 1 °
2π‘₯ + 1 °
10. Find the measure of ∑𝐴 below.
Geometry Chapter 4 Test Review
Congruent Triangles
Name:
Date:
Period:
11. The measure of ∑𝐡 is _____.
[A] 89°
[B] 99°
[C] 101°
[D] 79°
12. If βˆ π‘ƒ β‰… βˆ‘π‘„ and π‘šβˆ‘π‘„ = 2π‘₯ + 4 and π‘šβˆ‘π‘ƒ = 34, what is the value of x?.
13. If βˆ†π‘…π‘ƒπ‘„ β‰… βˆ†π½πΎπΏ, then 𝐿𝐽 β‰…_____ . 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 45ο‚°
D. A triangle with two acute angles and one obtuse angle
16. In the diagram, ∑𝐡 β‰… ∑𝐸 and ∑𝐢 β‰… ∑𝐹. Find the value of x.
B
A
π‘₯ + 50 ° 35° C
D
75°
F
E
Geometry Chapter 4 Test Review
Congruent Triangles
Name:
Date:
Period:
17. Refer to the figure below. Which of the following statements is true?
E
G
D
F
DEF is equilateral 𝐷𝐺 β‰… 𝐹𝐺
[A] βˆ†π·πΊπΈ β‰… βˆ†πΉπΊπΈ by SSS
[B] βˆ†π·πΌπΊ β‰… βˆ†πΉπΌπΊ by SAS
[C] βˆ†π·πΉπΊ β‰… βˆ†πΊπΈπ· by SSS
[D] There are no congruent triangles.
18. State two postulates or theorems that can be used to conclude that βˆ†π΄π‘‚π΅ β‰… βˆ†πΆπ‘‚π·.
19. Refer to the figure shown. Which of the following statements is true?
U
V
W
T
TV  WV
UV  XV
X
[A] βˆ†π‘‡π‘ˆπ‘‰ β‰… βˆ†π‘‰π‘Šπ‘‹ by SAS
[B] βˆ†π‘‡π‘ˆπ‘‰ β‰… βˆ†π‘Šπ‘‹π‘‰ by SAS
[C] βˆ†π‘‡π‘ˆπ‘‰ β‰… βˆ†π‘‹π‘Šπ‘‰ by ASA
[D] βˆ†π‘‡π‘ˆπ‘‰ β‰… βˆ†π‘Šπ‘‹π‘‰ by ASA
Geometry Chapter 4 Test Review
Congruent Triangles
Name:
Date:
Period:
20. Which postulate or theorem can be used to determine the measure of 𝑅𝑇?
21. Given:∑𝐡 β‰… ∑𝐸 and ∑𝐢 β‰… ∑𝐹. What other piece of information is needed to show
βˆ†π΄π΅πΆ β‰… βˆ†π·πΈπΉ by ASA Congruence Postulate?
[A] ∑𝐴 β‰… ∑𝐷
[B] 𝐡𝐢 β‰… 𝐸𝐹
[C] ∑𝐡 = ∑𝐹
[D] 𝐸𝐹 β‰… 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
24. In βˆ†π΄π΅πΆ, 𝐴𝐡 β‰… 𝐡𝐢 , 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
Name:
Date:
Period:
26. Use information in the figure below to find π‘šβˆ‘π·.
E
101°
D
F
27. βˆ†π΄π΅π· β‰… βˆ†πΆπ΅π·. Name the theorem or postulate that justifies the congruence.
A
B
D
C
28. Refer to the figure below.
A. Is there enough information to know whether ∑𝐹𝐸𝐺 is acute, obtuse, or a
right angle? Explain.
B. If π‘šβˆ‘πΉ is less than 45°, what type of angle is ∑𝐹𝐸𝐺? Explain.
29. Find the measure of ∑𝐡.
49°
128°
B
Geometry Chapter 4 Test Review
Congruent Triangles
Name:
Date:
[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
Period:
[14] d = 5.5, e = 33, f = 90, g = 57,
h = 10.1
[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°
[24] [A]
[25] π‘₯ = 44°, 𝑦 = 68°
[26] 39.5°
[27] AAS
[28] Look below for proof.
[28] 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.
[29] 79°