Proving Triangles are Congruent: SSS and SAS Chapter 4.3

Postulate 19: (SSS) Side-Side-Side Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. Goal 1: SSS & SAS Congruence Postulates Side BC EF, and

Proof

Postulate 20: (SAS) Side-Angle-Side Congruence Postulate If two sides and the included angle of one triangle are congruent to two sides and the included of a second triangle, then the two triangles are congruent. PQS XYZ If Side QS YZ, Side PS XZ,

Proof

Example 3: Choosing Which Congruence Postulate to Use Goal 2: Modeling a Real Life Situation Paragraph Proof The marks on the diagram show that PQ  PS and QR  SR. By the Reflexive Property of Congruence, RP  RP. Because the sides of ΔPQR are congruent to the corresponding sides of ΔPSR, you can use the SSS Congruence Postulate to prove that the triangle are congruent.

Example 6: Congruent Triangles in a Coordinate Plane Use the SSS Congruence Postulate to show that ABC FGH. A(-7,5) C(-4,5) B(-7,0) G(1,2) H(6,5) F(6,2) **Use the Distance Formula to find the lengths BC and GH** AC = FH = 3 AB = FG = 5 AB FG Who remembers the distance formula? BC = GH = √34 All sides congruent