Chapter 5 Congruent Triangles

Section 2 Proving Triangles are Congruent: SSS and SAS

Example 1: Use the SSS Congruence Postulate Does the diagram given enough information to show that the triangles are congruent? Explain.

Example 2: Use the SAS Congruence Postulate Does the diagram give enough information to use the SAS Congruence Postulate? Explain your reasoning. a) b)

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.

Example 3: Write a Proof Write a two-column proof that shows ∆𝐽𝐾𝐿≅∆𝑁𝑀𝐿 Example 3: Write a Proof Write a two-column proof that shows ∆𝐽𝐾𝐿≅∆𝑁𝑀𝐿. Statements Reasons 1) 1) 2) 2) 3) 3) 4) 4) 5) 5)

Example 4: Prove Triangles are Congruent You are making a model of the window shown in the photo. You know that DR ⊥ AG and RA ≅ RG. Write a proof to show that ∆𝐷𝑅𝐴≅∆𝐷𝑅𝐺. Statements Reasons 1) 1) 2) 2) 3) 3) 4) 4) 5) 5) 6) 6)

Checkpoint: Prove Triangles are Congruent Fill in the missing statements and reasons.

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