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Proving Triangle Congruence Using the SSS Postulate

Explore 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. This guide will show you how to apply the SSS postulate with examples, including the use of the distance formula to calculate the lengths between vertices. You'll also learn how to construct congruent triangles based on given side lengths. Understanding the SSS postulate is essential for geometry and helps establish fundamental concepts in triangle congruence.

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Proving Triangle Congruence Using the SSS Postulate

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  1. Prove Triangles Congruent by SSS

  2. Prove Triangles Congruent by SSS • Side-Side-Side (SSS) Congruence Postulate:

  3. Prove Triangles Congruent by SSS • Side-Side-Side (SSS) Congruence Postulate: • If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

  4. Prove Triangles Congruent by SSS • Side-Side-Side (SSS) Congruence Postulate: • If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. • In other words:

  5. Prove Triangles Congruent by SSS • Side-Side-Side (SSS) Congruence Postulate: • If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. • In other words: • If all the sides are the same, the triangles are the same.

  6. Prove Triangles Congruent by SSS • Side-Side-Side (SSS) Congruence Postulate: • If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. • In other words: • If all the sides are the same, the triangles are the same.

  7. Prove Triangles Congruent by SSS • Given: • KL = NL, KM = NM • Prove KLM = NLM L K N M

  8. Prove Triangles Congruent by SSS 8 8 8 4 6 6

  9. Prove Triangles Congruent by SSS • Show how you know LMA = LOA M L A O

  10. Prove Triangles Congruent by SSS • Using the distance formula:

  11. Prove Triangles Congruent by SSS • Using the distance formula: • With a set of points use the distance formula to find the length between two points.

  12. Prove Triangles Congruent by SSS • Using the distance formula: • With a set of points use the distance formula to find the length between two points. • JKL has vertices J (-3, -2) K (0, -2) L (-3, -8) • RST has vertices R (10, 0) S (10, -3) T (4, 0)

  13. Prove Triangles Congruent by SSS • Using the distance formula: • With a set of points use the distance formula to find the length between two points. • JKL has vertices J (-3, -2) K (0, -2) L (-3, -8) • RST has vertices R (10, 0) S (10, -3) T (4, 0) • Find out if the triangles are congruent.

  14. Prove Triangles Congruent by SSS • Using the distance formula: • With a set of points use the distance formula to find the length between two points. • JKL has vertices J (-3, -2) K (0, -2) L (-3, -8) • RST has vertices R (10, 0) S (10, -3) T (4, 0) • Find out if the triangles are congruent.

  15. Prove Triangles Congruent by SSS • How to construct a congruent triangle.

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