Proving Triangles Congruent: ASA and AAS

1
Proving Triangles CongruentASA and AAS

• 8.2

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Postulate 8-3ASA

• If two angles and the included side of one
  triangle are congruent to two angles and the
  included side of another triangle then the two
  triangles are congruent.

3
Example

• Given ltCAB ltDAE, AB AE and ltABC and ltAED are
  right angles prove ABC AED
• You can use ASA here to prove the two triangles
  congruent.

C
D
A
B
E
4
Theorem 8-1AAS

• If two angles and a non-included side of one
  triangle and congruent to two angles and the
  corresponding non-included side of another
  triangle then the triangles are congruent.

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Example II

• Given XQ TR and XR bisects QT prove triangle
  XMQ RMT

Q
X
M
R
T
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Example II Cont

• Statements
• 1) XQ TR
• 2) ltQ ltT
• 3) ltX ltR
• 4) XR bisects QT
• 5) TM QM
• 6) XMQ RMT

• Reasons
• 1) Given
• 2) if then AIA are
• 3) if then AIA are
• 4) Given
• 5) Def. segment bisector
• 6) AAS

7
Homework

• P 416 1-14, 18,20,27-29