Sec' 43 Triangle by ASA and AAS

1
Sec. 4-3Triangle ? by ASA and AAS

• Objective
• 1) To prove 2 ?s ? using the ASA postulate and
  the AAS thereom.

2
Are these triangles congruent?
review
13
12
13
5
12
5

• Yes(SSS Congruence Conj.)

3
Are these triangles congruent?
review
3
5
5
4
4
3

• Yes(SSS Congruence Conj.)

4
Are these triangles congruent?
review
7
7
9
9

• Yes(SAS Congruence Conj.)

5
Are these triangles congruent?
13
13
97
89
87
95
review

• NO

6
Are these triangles congruent?
12
5
19
19
5
12
review

• Yes(SAS Congruence Conj.)

7
Which shortcut talked about today does not
necessarily prove triangle congruency?

• SSA

review
8
P(4-3) ASA (Angle Side Angle)

• If 2 ?s and the included side of one ? are ? to
  two ?s and the included side of another ?, then
  the ?s are ?.

A
S
D
R
C
T
Congruence Statement ?CDA ?
?TRS
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Proof

• Given PQ ? QS
• ?P ? ?S
• Prove ?PQT ? ?SQR

P
R
Q
T
S
Statement 1) PQ ? QS 2) ?P ? ?S 3) ?PQT ?
?SQR 4) ?PQT ? ?SQR

• Reasons
• Given
• Given
• Def. of Vertical ?
• ASA

S
A
A
10
Th. (4-2) AAS (Angle Angle Side)

• If 2 ?s and a non-included side of one ? are ? to
  2 ?s and the corresponding non-included side of
  another ?, then the ?s are ?.

N
H
P
J
M
L
Congruence Statement ?HJL ?
?NPM
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Proof
B
A

• Given ?D ? ?B
• AB // DC
• Prove ?ABC ? ?CDA

D
C

• Reasons
• Given
• Given
• Alt. Int. ?s are ?
• Reflexive Prop
• AAS

• Statements
• 1) ?D ? ?B
• AB // DC
• ?BAC ? ?ACD
• AC ? AC
• ?ABC ? ?CDA

A
A
S
12
Are these triangles congruent?
60
6
6
60
5
5
60
60
60
60
5
6

• NO

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