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Transcript
```Geometry Honors: Chapter 4 Test
2. Complete the proof by giving the missing
reasons
Given:
Prove:
N
F
B
V
Statement
1.
2.
Reason
1. Given
3.
4.
5.
3.
?
4. Reflexive Property
5.
?
?
2.
?
3. Supply the missing reasons to complete the proof.
Given:
and
Prove:
S
U
T
R
V
4. Is there enough information to prove the two triangles congruent? If yes, write the congruence statement and name
the postulate you would use. If no, write not possible and tell what other information you would need.
Q
|
|
(
)
S
P
R
5. Supply the reasons missing from the proof shown below.
Given:
,
Prove:
|
|
(
(
A
B
D
C
6. Justify the last two steps of the proof.
Given:
and
Prove:
xº
M
N
58°
O
Drawing not to scale
10. What is the value of x?
P
E
Proof:
1.
1. Given
3.
4.
7. Given
|
2. Given
3.
4.
2.
xº
and
, find
B
|
C
D
|
9. What is the value of x?
E
|
108.5°
F
Drawing not to scale
and
8. What additional information will allow you to
prove the triangles congruent by the HL Theorem?
A
D
11.
12. Two sides of an equilateral triangle have lengths
and
. Which could be the length of
the third side:
or
?
13. If BCDE is congruent to OPQR, then
congruent to
5
5
is
14. State whether
and
are congruent.
15. What is the missing reason in the two-column proof?
Given:
Prove:
bisects
and
bisects
N
<
M
O
>
P
Statements
Reasons
1.
2.
3.
1. Given
2. Definition of angle bisector
3. Reflexive property
bisects
4. Given
5. Definition of angle bisector
6.
?
4.
bisects
5.
6.
16. What is the value of x?
A
(
(
34°
21
|
21
|
y°
x°
xº
Drawing not to scale
B
65°
D
C
Drawing not to scale
17. Find the values of x and y.
18. The two triangles are congruent as suggested by
their appearance. Find the value of g. The diagrams
are not to scale.
M
N
d°
30°
g
25
b
f°
e°
24
60°
7
c
P
19. Given
and
, find the length of QS and TV.
20. What else must you know to prove the triangles
congruent by ASA? By SAS?
23. What other information do you need in order to
prove the triangles congruent using the SAS
Congruence Postulate?
B
A
(
A
(
C
D
B
21. What common angle do
B
C
D
24. Find the value of x. The diagram is not to scale.
S
C
A
|
|
F
(2 x – 30)°
R
G
22. Name the angle included by the sides
and
(8 x )°
T
U
25. Which triangles are congruent by ASA?
F
(
A
V
T ))
|
|
G
)
B
C
D
H
U
A
((
B
(
C
26. Is there enough information to conclude that the
two triangles are congruent? If so, what is a correct
congruence statement?
Multiple Choice
Identify the choice that best completes the statement or answers the question.
27. Based on the given information, what can you
28. R, S, and T are the vertices of one triangle. E, F,
conclude, and why?
and D are the vertices of another triangle.
RS
Given:
= 4, and EF = 4. Are the two triangles congruent? If
yes, explain and tell which segment is congruent to
F
H
A.
B.
C.
D.
G
E
A.
B.
C.
D.
I
by ASA
by ASA
by SAS
by SAS
yes, by AAS;
yes, by ASA;
yes, by SAS;
No, the two triangles are not congruent.
29. Can you use the SAS Postulate, the AAS Theorem,
or both to prove the triangles congruent?
A.
B.
C.
D.
SAS only
either SAS or AAS
AAS only
neither
30. If
and