Prove Triangles Congruent by ASA &

AAS

Lesson 4.10 (M1)Use two more methods to prove triangle congruence

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.

ASA Congruence Postulate

AAS Congruence Theorem

GUIDED PRACTICE for Examples 1 and 2

SOLUTION

1.

GivenS U

The vertical angles are congruent

RTS UTV

GivenRS UV

STATEMENTS REASONS

In the diagram at the right, what postulate or theorem can you use to prove that RST VUT ? Explain.

GUIDED PRACTICE for Examples 1 and 2

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

ANSWER

GUIDED PRACTICE for Examples 1 and 2

2.

1. Draw BD parallel to AC . 1. Parallel Postulate

PROVE 3 = 180°1m 2m m+ +

2. Angle Addition Postulate and definition of straight angle

2. 4m 2m 5m+ + = 180°

3. Alternate Interior Angles Theorem

3. 1 4 , 3 5

5. Substitution Property of Equality

5. 1m 2m 3m+ + = 180°

4. Definition of congruent angles

4. 1m = 4m 3m = 5m,

STATEMENTS REASONS

GIVEN ABC