3.7 Worksheet

Name Class Date Practice
Form G
Congruence in Overlapping Triangles
For Exercises 1–6, separate and redraw the indicated triangles. Identify any
common angles or sides.
1.△ABC and △DCB
B
A
G
F
C
3. △JML and △NKL
2. △EFG and △HGF
L
E
4.△BYA and △CXA
H
J
6. △MPN and △MOQ
5. △GEH and △FEH
B
M
G
F
D
A
N
K
D
X
M
M
Y
E
C
H
N
O
P
Q
In each diagram in Exercises 7–12 the given triangles are congruent. Identify
their common side or angle.
7.△ADC and △BCD
A
8. △KNJ and △KML
B
U
K
M
C
D
9. △UXV and △VWU
10. △QTR and △SRT X
N
J
V
W
L
11. △EGH and △EGF
12. △YNI and △YPZ
Y
E
Q
Z
T
R
H
G
F
N
S
13. Open-Ended Draw a diagram of a pair of triangles that share
a common angle and a common side.
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
I
P
Name Class Date Practice (continued)
Form G
Congruence in Overlapping Triangles
14. Complete the following proof.
R
Given: RU ≅ TS, ∠RUT and ∠UTS are right angles, V is the
midpoint of US.
S
V
Prove: △RVU ≅ △TVS
U
Statements
Reasons
1) RU ≅ TS, ∠RUT and ∠UTS are
right angles, V is the midpoint of US.
1) ?
2) UT ≅ TU
3) ?
2) ?
4) ?
5) ∠RUS and ∠SUT are
complementary angles.
6) ?
7) ∠SUT ≅ ∠RTU
8) ∠RUS ≅ ∠STR
9) ?
T
3) All right angles are congruent
4) SAS
5) ?
6) Definition of complementary angles
7) ?
10) ∠RVU ≅ ∠TVS
8) ?
9) Definition of midpoint
10) ?
11) △RVU ≅ △TVS
11) ?
15. Write a paragraph proof.
M
Given: P is the midpoint of QN , MP # QN
R
Prove: △MRQ ≅ △MRN
Q
P
F
16. In the diagram at the right, ∠A ≅ ∠C, AB ≅ CE,
D
and DA ≅ FC. Which two triangles are congruent
by SAS? Explain.
A
B
E
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
C
N

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