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4.3 – Prove Triangles Congruent by SSS

4.3 – Prove Triangles Congruent by SSS. Geometry Ms. Rinaldi. Side-Side-Side (SSS) Congruence Postulate. B. If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. If Side Side Side Then. C. A. S. T. R. EXAMPLE 1.

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4.3 – Prove Triangles Congruent by SSS

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  1. 4.3 – Prove Triangles Congruent by SSS Geometry Ms. Rinaldi

  2. Side-Side-Side (SSS) Congruence Postulate B If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. If Side Side Side Then C A S T R

  3. EXAMPLE 1 Use the SSS Congruence Postulate Decide whether the congruence statement is true. Explain your reasoning. SOLUTION Given Given Reflexive Property So, by the SSS Congruence Postulate,

  4. ACBCAD It is given that BC AD By Reflexive property AC AC, But AB is not congruent CD. Therefore, the triangles are not congruent. Use the SSS Congruence Postulate EXAMPLE 2 Decide whether the congruence statement is true. Explain your reasoning. SOLUTION

  5. DFGHJK Use the SSS Congruence Postulate EXAMPLE 3 Decide whether the congruence statement is true. Explain your reasoning.

  6. Use the SSS Congruence Postulate EXAMPLE 4 Decide whether the congruence statement is true. Explain your reasoning. A B C D

  7. Use the SSS Congruence Postulate EXAMPLE 5 Decide whether the congruence statement is true. Explain your reasoning. A B C D

  8. Use the SSS Congruence Postulate EXAMPLE 6 has vertices J(-3, -2), K(0, -2), and L(-3, -8). has vertices R(10, 0), S(10, -3), and T(4, 0). Graph the triangles in the same coordinate plane and show that they are congruent. SOLUTION Use the distance formula to find the lengths of the diagonal segments. LK = TS =6.7 (By distance formula) KJ = SR =3. (By counting) JL = RT =6. (By counting) Therefore, by SSS, the triangles are congruent.

  9. Use the SSS Congruence Postulate EXAMPLE 7 has vertices P(-5, 4), Q(-1, 4), and R(-1, 1). has vertices A(2, 5), B(2, 1), and C(5, 1). Graph the triangles in the same coordinate plane and show that they are congruent. STEP 1: Graph STEP 2: Use the distance formula to find the lengths of the diagonal segments. PR = AC = PR = _____ =______(By ______________) PQ =_____ = _____ (By_____________) QR = _____ = _____ (By ____________) Therefore, by ______, _________________________.

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