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Understanding SSS Congruence Postulate in Triangles

This article delves into the SSS (Side-Side-Side) Congruence Postulate, which states that if three sides of one triangle are congruent to three sides of another triangle, the two triangles are congruent. We discuss proof techniques using the Reflexive Property and provide guided practice examples to solidify understanding. Additionally, we explore scenarios where congruences are not true, emphasizing the importance of corresponding sides. This resource is aimed at students looking to enhance their understanding of triangle congruence.

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Understanding SSS Congruence Postulate in Triangles

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  1. Write a proof. GIVEN KL NL,KM NM PROVE KLMNLM Proof KL NL andKM NM It is given that LM LN. By the Reflexive Property, So, by the SSS Congruence Postulate, KLMNLM EXAMPLE 1 Use the SSS Congruence Postulate

  2. DFGHJK SideDG HK, SideDF JH,andSideFG JK. So by the SSS Congruence postulate, DFG HJK. for Example 1 GUIDED PRACTICE Decide whether the congruence statement is true. Explain your reasoning. SOLUTION Three sides of one triangle are congruent to three sides of second triangle then the two triangle are congruent. Yes. The statement is true.

  3. ACBCAD 2. GIVEN : BC AD ACBCAD PROVE : It is given that BC AD By Reflexive property AC AC, But AB is not congruent CD. PROOF: for Example 1 GUIDED PRACTICE Decide whether the congruence statement is true. Explain your reasoning. SOLUTION

  4. for Example 1 GUIDED PRACTICE Therefore the given statement is false and ABC is not Congruent to CAD because corresponding sides are not congruent

  5. 3. QPTRST GIVEN : QT TR , PQ SR, PT TS PROVE : QPTRST It is given that QT TR, PQ SR, PT TS.So by SSS congruence postulate, QPT RST. Yes the statement is true PROOF: for Example 1 GUIDED PRACTICE Decide whether the congruence statement is true. Explain your reasoning. SOLUTION

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