1. EXAMPLE 1
Identify congruent triangles
Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use.
SOLUTION
The vertical angles are congruent, so two pairs of angles and a pair of non-included sides are congruent. The triangles are congruent by the AAS Congruence Theorem.

2. EXAMPLE 1
Identify congruent triangles
There is not enough information to prove the triangles are congruent, because no sides are known to be congruent.
Two pairs of angles and their included sides are congruent. The triangles are congruent by the ASA Congruence Postulate.

3. EXAMPLE 2
Prove the AAS Congruence Theorem
Prove the Angle-Angle-Side Congruence Theorem.
Write a proof.
GIVEN
BC EF
A D,
C F,
PROVE
ABC DEF

4. 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

5. 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

6. GUIDED PRACTICE for Examples 1 and 2
Rewrite the proof of the Triangle Sum Theorem on page 219 as a flow proof.
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°