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Proving Triangles are Congruent: SSS and SAS

Proving Triangles are Congruent: SSS and SAS. Chapter 4.3. Objectives/Assignment. Prove that triangles are congruent using the SSS and SAS congruence postulate Use congruence postulates in real life problems Assignment: 2-28 even, 44-46 all. Goal 1: SSS & SAS Congruence Postulates.

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Proving Triangles are Congruent: SSS and SAS

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  1. Proving Triangles are Congruent:SSS and SAS Chapter 4.3

  2. Objectives/Assignment • Prove that triangles are congruent using the SSS and SAS congruence postulate • Use congruence postulates in real life problems • Assignment: 2-28 even, 44-46 all

  3. Goal 1: SSS & SAS Congruence Postulates 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. Side BCEF, and

  4. Proof

  5. 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. If Side QSYZ, Side PSXZ, PQS XYZ

  6. Proof

  7. Goal 2: Modeling a Real Life Situation Example 3: Choosing Which Congruence Postulate to Use 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.

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

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