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Understanding the Side-Side-Side (SSS) Congruence Postulate in Triangles

The Side-Side-Side (SSS) Congruence Postulate states that if all three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. This postulate is fundamental in triangle congruence and has several applications in geometry. In this resource, we explore examples demonstrating the SSS postulate, solve triangle congruence problems, and clarify the conditions under which two triangles can be deemed congruent. Engage with interactive exercises to reinforce your understanding.

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Understanding the Side-Side-Side (SSS) Congruence Postulate in Triangles

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  1. Triangle Congruency MM1G3c

  2. Congruency Postulates/Theorems

  3. SSS Congruency Postulate

  4. Side-Side-Side (SSS) Congruence Examples

  5. The Side-Side-Side (SSS) Congruence Postulate states that if all three sides of one triangle are congruent to all three sides of another triangle, then the two triangles are congruent. D A E B F C

  6. Example 1: In the triangles below, MN = 3, NP = 4, MP = 5, XY = 3, YZ = 4, and XZ = 5. Are the two triangles congruent? If so, why? Solution: M X N P Y Z

  7. Example 2: If x = 4, are the two triangles below congruent? If so, why? Solution: Substituting x = 4, we can find the length of each side. QP = 10, QR = 12, and PR = 9 KL = 10, KJ = 12, and LJ = 9 Q K 2x+2 5x-8 3x x+6 P R J L 2x+1 3x-3

  8. Example 3: Is ∆ ABD congruent to ∆ CDB? If so, why? Solution: A B D C

  9. K Q 10 12 12 10 P R J L 9 9 Therefore, since all three sides of ∆ QPR are congruent to all three sides of ∆ KLJ, then the two triangles are congruent by the Side-Side-Side (SSS) Congruence Postulate.

  10. Summary Side-Side-Side (SSS) Congruence Postulate: If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

  11. Interactive Website! • SSS Congruency

  12. Try These: C

  13. Try These: D

  14. Try These: D

  15. Try These: D

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