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Lesson 5.3 Proving Triangles are Congruent: ASA and AASPowerPoint Presentation

Lesson 5.3 Proving Triangles are Congruent: ASA and AAS

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### Lesson 5.3 Proving Triangles are Congruent: ASAand AAS

Pages 250 - 252

Angle-Side-Angle Congruence Postulate (ASA)

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

Angle– B ≅ M

Side – BO≅MA

Angle– O≅A

Therefore, by ASA, BOW ≅ MAN

M

B

A

N

O

W

Angle-Angle-Side Congruence Postulate (AAS)

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 triangles are congruent.

Angle– B ≅ M

Angle - O ≅ A

Side – BW ≅MN

Therefore, by AAS, BOW ≅ MAN

M

B

A

N

O

W

Writing Proofs

A proof is a convincing argument that shows why a statement is true. A two-column proof has numbered statements and reasons that show the logical order of the argument. Each statement has a reason listed to its right.

How to Write a Proof

- List the given information first
- Use the information from the diagram
- Give a reason for every statement
- Use given information, definitions, postulates, and theorems as the “Reasons”
- List statements in order.
- End the proof with the statement that you are trying to prove.

Write a 2-Column Proof that shows JKL ≅ NML

Given: JK ≅MNand J ≅ N

Prove: JKL ≅ NML

Statements:Reasons:

1. 1.

2. 2.

3. 3.

4. 4.

J

M

L

K

N

Write a 2-Column Proof that shows DRA ≅ DRG

Given: A≅ G, R ≅ R, R is the midpoint of AG

Prove: DRA ≅ DRG

Statements:Reasons:

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

.

D

R

G

A

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