4.3 proving triangles are congruent

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4.3 proving triangles are congruent

  1. 1. Proving Triangles are Congruent SSS and SAS Congruence Postulates
  2. 2. ∠A P≅ ∠ ∠B Q≅ ∠ ∠C R≅ ∠ Corresponding AnglesCorresponding Sides PQAB ≅ QRBC ≅ PRAC ≅ ∆ABC ∆≅ PQR
  3. 3. Do we need to use all six pairs to prove two triangles are congruent? Proving Triangles are Congruent
  4. 4. SSS (Side-Side-Side) Congruence Postulate • If three sides of one triangle are congruent to three sides of a second triangle, the two triangles are congruent. If Side PQAB ≅ QRBC ≅ PRAC ≅ ∆ABC ∆≅ PQR Then Side Side
  5. 5. Example 1 Prove: ∆DEF ∆≅ JKL From the diagram, .,, KLEFandJLDFJKDE ≅≅≅ SSS Congruence Postulate.∆DEF ∆≅ JKL
  6. 6. • If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. SAS (Side-Angle-Side) Congruence Postulate
  7. 7. Example 2 Prove: ∆SYT ∆≅ WYX
  8. 8. Which Congruence Postulate to Use? 1. Decide whether enough information is given in the diagram to prove that triangle PQR is congruent to triangle PQS. If so give a two-column proof and state the congruence postulate.
  9. 9. Checkpoint Decide if enough information is given to prove the triangles are congruent. If so, state the congruence postulate you would use.
  10. 10. Congruent Triangles in the Coordinate Plane Use the SSS Congruence Postulate to show that ∆ABC ∆≅ DEF Which other postulate could you use to prove the triangles are congruent?
  11. 11. Closure Question
  12. 12. Homework • Exercise 4.3 page 216: 1-19, 20, 21-27, 33, 35 odd.

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