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Contents Lesson 4-1Classifying Triangles Lesson 4-2Angles of Triangles Lesson 4-3Congruent Triangles Lesson 4-4Proving Congruence–SSS, SAS Lesson 4-5Proving Congruence–ASA, AAS Lesson 4-6Isosceles Triangles Lesson 4-7Triangles and Coordinate Proof

Lesson 4 Contents Example 1Use SSS in Proofs Example 2SSS on the Coordinate Plane OBJECTIVE: To use the SSS Postulate to test for triangle congruence (2.9.8K) (M8.C.1.1) POSTULATE 4.1 – Side-Side-Side Congruence: If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent (SSS).

Example 4-1a ENTOMOLOGY The wings of one type of moth form two triangles. Write a two-column proof to prove that  FEG  HIG and G is the midpoint of both

Example 4-1b Given: G is the midpoint of both Prove: 1. Given1. Proof: ReasonsStatements 3. SSS 3.  FEG  HIG  FEG  HIG 2. Midpoint Theorem2.

Example 4-1b 3. SSS 1. Given 2. Reflexive Proof: ReasonsStatements  ABC  GBC Write a two-column proof to prove that  ABC  GBC if

Example 4-2a Use the Distance Formula to show that the corresponding sides are congruent. COORDINATE GEOMETRY Determine whether  WDV  MLP for D(–5, –1), V(–1, –2), W(–7, –4), L(1, –5), P(2, –1), and M(4, –7). Explain.

Example 4-2b Answer: By definition of congruent segments, all corresponding segments are congruent. Therefore,  WDV  MLP by SSS.

Example 4-2c Answer: By definition of congruent segments, all corresponding segments are congruent. Therefore,  ABC  DEF by SSS. Determine whether  ABC  DEF for A(5, 5), B(0, 3), C(–4, 1), D(6, –3), E(1, –1), and F(5, 1). Explain.

End of Lesson 4

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