Download Geometry: Unit 3 Review

Geometry: Unit 3 Review
Name: ______________________________
Date: _________________ Hour: ____
Identify the choice that best completes the statement or answers the question.
____ 1. In each pair of triangles, parts are congruent as marked. Which pair of triangles is
congruent by ASA?
a.
c.
b.
d.
____ 2. Name the theorem or postulate that lets you immediately conclude
A
B
(
(
D
C
a. ASA
b. AAS
c. SAS
d. none of these
____ 3. Where can the bisectors of the angles of an obtuse triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
a. I only
b. III only
c. I or III only
d. I, II, or II
____ 4. Where can the medians of a triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
a. I only
b. III only
c. I or III only
d. I, II, or II
____ 5. Which group contains triangles that are all similar?
a.
b.
13
7
7
) 32°
7
)
45°
7
) 53°
53°
)
) 45°
d.
c.
____ 6. In the diagram below,
bisects
9
.
Which of these would be necessary to justify that
Angle-Side-Angle Congruency Theorem?
a.
c.
b.
d.
is congruent to
by the
bisects
____ 7. Emilio had a map of the zoo. He noticed that when he
connected the points for the places he wanted to go to, it
created two similar triangles.
Using the given diagram, which of the
following explains why
?
a. Angle-Angle Similarity Postulate
c.
Side-Side-Side Similarity Postulate
b. Side-Angle-Side Similarity Postulate
d.
Transitive Property of Similarity.
8
____ 8. Which steps correctly state how to construct the circumscribed circle (also called
circumcircle) of a triangle?
a.
.
b.
To find the center of the
To find the center of the
c.
circumscribed circle, find the point
circumscribed circle, find the point
of concurrence of the three internal
of concurrence of the three
angle bisectors. The radius of the
altitudes. The radius of the circle is
circle is the segment that joins the
the segment that joins the center
center and one side of the triangle
and one of the vertices of the
and is perpendicular to the side.
triangle.
To find the center of the
To find the center of the
d.
circumscribed circle, find the point
circumscribed circle, find the point
of concurrence of the three
of concurrence of the three
medians of the triangle. The radius
perpendicular bisectors. The radius
of the circle is the segment that
of the circle is the segment that
joins the center and one of the
joins the center and one of the
vertices of the triangle.
vertices of the triangle.
Short Answer
9. Classify the triangle by its sides. The diagram is not to scale.
9
7
9
10. Classify
ABC by its angles, when m A = 36, m B = 89, and m C = 55.
11. The triangular playground has angles whose measures are in the ratio 7 : 2 : 3. What
is the measure of the smallest angle?
61°
12. Find the value of x. The diagram is not to scale.
106°
x°
119°
13. Find the value of the variable. The diagram is not to scale.
49°
x°
14. If BCDE is congruent to OPQR, then
is congruent to
U
V
15. Use the information given in the diagram. Tell why
and
X
W
16.
17. The two triangles are congruent as suggested by their appearance. Find the value of
d. The diagrams are not to scale.
d°
21°
g
25
b
f°
e°
7
18. Given
24
69°
c
and
, find the length of QS and TV.
N
19. Name the angle included by the sides
M
and
P
20. Justify the last two steps of the proof.
Given:
Prove:
R
and
S
Proof:
1.
2.
1. Given
3.
4.
3.
4.
T
2. Given
U
A
(
(
21. Find the values of x and y.
|
|
y°
x°
B
54°
D
C
Drawing not to scale
22. What is the measure of the vertex angle of an isosceles triangle if one of its base
angles measures 58°?
E
|
23. Use the information in the figure. Find
D
106°
|
F
Drawing not to scale
24. What additional information will allow you to prove the triangles
congruent by the HL Theorem?
A
B
|
C
D
|
E
36
25. Find the value of x. The diagram is not to scale.
x
36
34
32
26. Points B, D, and F are midpoints of the sides of
The diagram is not to scale.
32
EC = 34 and DF = 19. Find AC.
A
B
F
C
E
D
27. Use the information in the diagram to determine the height of the tree. The diagram
is not to scale.
190 ft
28. In
ABC, G is the centroid and BE = 12. Find BG and GE.
C
B
A
C
|
29. Name a median for
G
)
|
F
)
E
H D
G
F
D
E
30. Name the point of concurrency of the angle bisectors.
31. Find the length of
, given that
is a median of the triangle and AC = 60.
D
A
B
C
32. For a triangle, list the respective names of the points of concurrency of
• perpendicular bisectors of the sides
• bisectors of the angles
• medians
• lines containing the altitudes.
33. What is the name of the segment inside the large triangle?
34. Find the area. The figure is not drawn to scale.
7 cm
4.4 cm
35. Figure
. Name a pair of corresponding sides?
36. ABCD ~ WXYZ. AD = 12, DC = 6, and WZ = 52. Find YZ. The figures are not drawn to
scale.
X
B
W
A
Z
C
D
Z
37. Triangles ABC and DEF are similar. Find the lengths of AB and EF.
A
D
5x
5
x F
E
B
4
C
38. Write a similarity statement for the triangles.
D
53°
G
60°
C
60°
E
F
67°
H
39. State whether the triangles are similar. If so, write a similarity statement and
the postulate or theorem you used.
B
5
O
12
5
7.5
A
M
8
7.5
C
N
40. Explain why the triangles are similar. Then find the value of x.
)
x
8
)
15
9
Not drawn to scale
Geometry: Unit 3 Review Answer Key
MULTIPLE CHOICE
22.
64°
23.
37°
1.
D
2.
A
3.
A
24.
4.
A
25.
68
5.
A
26.
38
6.
A
27.
95 ft
7.
A
28.
8. D
29.
SHORT ANSWER
9.
isosceles
10.
acute
11.
30
12.
45
13.
12
30.
31.
32.
34. 15.4 cm2
Reflexive Property, Given
16.
21
18.
10
37. AB = 10; EF = 2
38.
19.
21.
35.
36. 26
17.
20.
circumcenter
incenter
centroid
orthocenter
33. angle bisector
14.
15.
C
30
39.
Reflexive Property of
; SSS
; SSS
40. AA Postulate; 4
4
5