Lesson 5.3 Proving Triangles are Congruent: ASA and AAS

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

Does the diagram show that the triangles are congruent by ASA? N P O M L K

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

Does the diagram give enough information to use the AAS Congruence Postulate? A L H R P R T S

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

Assignment: Pages 254 – 256 #14 – 26 even, #34, #38 – 44 even and 5.3 Practice B worksheet

Lesson 5.3 Proving Triangles are Congruent: ASA and AAS