Math 8 – congruent triangles
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This document discusses congruent triangles and the corresponding parts theorem. It defines the three postulates used to prove congruence: SSS, SAS, and ASA. It provides an example of using the SSS postulate and corresponding parts theorem to show that two angles are congruent and find the exact measure of one of the angles. It emphasizes that corresponding parts theorem can only be used after triangles are shown to be congruent.
Math 8 – congruent triangles
- 1. Math 8 – Congruent Triangles Ms. Andi Fullido © Quipper
- 2. Objectives •At the end of this lesson, you should be able to identify corresponding congruent parts of congruent triangles.
- 3. What are the three postulates used in proving that two angles are congruent? •SSS •SAS •ASA
- 4. Theorem: Corresponding parts of congruent triangles are congruent (CPCTC).
- 5. Theorem: Corresponding parts of congruent triangles are congruent (CPCTC). • What postulate?
- 6. The following triangles are congruent by the SSS Postulate. •If m∠B=2x−5 and m∠Y=3x−65, what is the exact measure of ∠B?
- 7. Since the two triangles are congruent, we know via CPCTC that: •Through the SSS postulate…. •∠A≅∠X •∠B≅∠Y •∠C≅∠Z
- 8. We need an equation to solve for the value of x. From CPCTC, ∠B and ∠Y are congruent or equal in measure, then we set both expressions equal to each other. •m∠B=m∠Y •2x−5=3x−65 •65−5=3x−2x •x=60
- 9. Use CPCTC in proofs only after showing that two triangles are congruent.
- 10. If both triangles ABC and PQR are said to be congruent, then ∠BAC is congruent to which angle?
- 11. Objectives •At the end of this lesson, you should be able to write two-column proofs involving congruent triangles.
- 12. Given: sBO≅sMA, sOW≅sAN, ∠O≅∠A Prove: △BOW≅△MAN
- 13. Proof