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Name
Class
Date
Practice
4-3
Form K
Triangle Congruence by ASA and AAS
Name the two triangles that are congruent by ASA.
1. S V
Q
R
2. A
T
U
B D
E
3.
L
X
C
Z
F
J
Y
N
O
H
G
K
kABC O kJKL
kRQS O kTUV
R
I
M
Q
P
kGHI O kMNP O kOQR
4. Developing Proof Complete the two-column proof
B
by filling in the blanks.
Given: BD ' AC, BD bisects /ABC
A
Prove: nABD > nCBD
Statements
C
D
Reasons
1) BD ' AC, BD bisects /ABC.
1) Given
2) 9 lADB and lCDB are right '. 2) Definition of perpendicular
3) /ADB > /CDB
3) 9 All right angles are O.
4) /ABD > /CBD
4) 9 Definition of l bisector
5) 9 BD O BD
5) Reflexive Property of >
6) 9 kABD O kCBD
6) ASA
5. Given: KJ > MN , /KJL > /MNL
K
M
Prove: nJKL > nNML
Statements
L
Reasons
J
1) KJ > MN , /KJL > /MNL
1) Given
2) /KLJ > /MLN
2) 9 Vertical ' are O.
3) 9 lLKJ O lLMN
3) Third Angles Theorem
4) 9 kJKL O kNML
4) ASA
Prentice Hall Foundations Geometry • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
25
N
Name
Class
4-3
Date
Practice (continued)
Form K
Triangle Congruence by ASA and AAS
6. Given: PT > RS, /PTR > /RSP
R
P
Prove: nPQT > nRQS
Statements
Q
Reasons
1) 9 PT O RS, lPTR O lRSP
1) Given
2) /PQT > /RQS
2) 9 Vertical ' are O.
3) 9 kPQT O kRQS
3) AAS
S
T
7. Given: BD is the angle bisector of /ABC and /ADC.
A
B
Prove: nABD > nCBD
C
Statements
Reasons
D
1) 9 BD is the angle bisector of
1) 9 Given
lABC and lADC.
2) 9 lABD O lCBD, lADB O lCDB 2) Definition of / bisector
3) /BAD > /BCD
3) 9 Third Angles Theorem
4) BD > BD
4) 9 Reflexive Property of O
5) 9 kABD O kCBD
5) AAS
8. Reasoning A student tells you that he can prove the AAS Theorem using the
SAS Postulate and the Third Angles Theorem. Do you agree with him? Explain.
(Hint: How many pairs of sides does the SAS Postulate use?)
No; answers may vary. Sample: the SAS Postulate requires two pairs of
corresp. O sides.
9. Reasoning Can you prove the triangles congruent?
Justify your answer.
No; answers may vary. Sample. there are no included
sides or included ' that correspond in both >, and you
cannot use the Third Angles Theorem.
Prentice Hall Foundations Geometry • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
26