1. Prove Triangles Congruent by ASA & AAS
Lesson 4.10 (M1)
Use two more methods to prove triangle congruence

2. Vocabulary
A flow proof uses arrows to show the flow of a logical argument.
ASA Congruence Postulate: If two angles and the included side of one triangle are congruent to two angles of a second triangle, then the two triangles are congruent
AAS Congruence Theorem: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.

3. ASA Congruence Postulate

4. AAS Congruence Theorem

7. GUIDED PRACTICE
for Examples 1 and 2
In the diagram at the right, what postulate or theorem can you use to prove that
RST VUT
? Explain.
SOLUTION
STATEMENTS
REASONS
Given
S U
Given
RS UV
The vertical angles are congruent
RTS UTV

8. GUIDED PRACTICE
for Examples 1 and 2
ANSWER
Therefore are congruent because vertical angles are congruent so two pairs of angles and a pair of non included side are congruent. The triangle are congruent by AAS Congruence Theorem.
RTS UTV

9. GUIDED PRACTICE for Examples 1 and 2 GIVEN ABC PROVE 3 = 180° 1 m 2 +
STATEMENTS
REASONS 1.
Draw BD parallel to AC .
Parallel Postulate 2.
Angle Addition Postulate and definition of straight angle 4 m 2 5 +
= 180° 3.
Alternate Interior Angles Theorem 1 4 , 3 5 4.
Definition of congruent angles 1 m = 4 3 5 , 5.
Substitution Property of Equality 1 m 2 3 +
= 180°