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Understanding the SSS Congruence Postulate in Geometry

This resource offers a comprehensive guide to the Side-Side-Side (SSS) Congruence Postulate, which states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. The document provides multiple examples, illustrating how to apply the SSS postulate to determine triangle congruence using reasoning and the distance formula. Detailed solutions emphasize the importance of congruency in geometry. Perfect for students looking to enhance their understanding of triangle properties and proofs.

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Understanding the SSS Congruence Postulate in Geometry

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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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