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Geometry

Learn how to use the Side-Side-Side (SSS) and Side-Angle-Side (SAS) postulates to test for triangle congruence. Includes examples and a two-column proof.

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Geometry

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  1. Geometry Notes Section 4-4

  2. What you’ll learn. . . . • How to use the SSS Postulate to test for triangle congruence • How to use the SAS Postulate to test for triangle congruence

  3. Vocabulary • Included angle

  4. Remember the Definition of Congruent Triangles • Two triangles are congruent if and only if their corresponding parts are congruent. • According to this definition we would have to show all six pairs of corresponding parts congruent to prove two triangles are congruent. • There has to be a shorter way. . .

  5. What is the minimum number of corresponding congruent parts necessary to show to triangles are congruent? • Would knowing all three pairs of sides congruent be enough? • This is called the Side-Side-Side (or SSS) Postulate

  6. Side-Side-Side Postulate: If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. • You can prove two triangles are congruent by showing they have sides of the same length.

  7. Example #1: Identify the congruent triangles in each figure.

  8. Example #2: Determine whether ΔDEF ΔPQR given the coordinates of the vertices. Explain. D(-6, 1), E(1, 2), F(-1, -4), P(0, 5), Q(7, 6), R(5, 0) You can show all 3 pairs of corresponding sides are congruent by using the distance formula.

  9. Example #2 (continued): Now for PQ, QR, and PR D(-6, 1), E(1, 2), F(-1, -4), P(0, 5), Q(7, 6), R(5, 0)

  10. Example 3: .

  11. Example #4:

  12. Example #5: Write a two-column proof.

  13. Might there be another shortcut combination of parts? Possibly mixing pairs of congruent sides with pairs of congruent angles? • Would knowing all two pairs of sides congruent and the angles between them be enough? • This is called the Side-Angle-Side (or SAS) Postulate

  14. Side-Angle-Side Postulate: If the two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. • You can prove two triangles are congruent by showing they have 2 sides and their included angles equal.

  15. Example #6: Identify the congruent triangles in each figure.

  16. Example #7: For each diagram, determine which pairs of triangles can be proved congruent by the SAS Postulate.

  17. Example #8: For each diagram, determine which pairs of triangles can be proved congruent by the SAS Postulate.

  18. Example #9: For each diagram, determine which pairs of triangles can be proved congruent by the SAS Postulate.

  19. Example #10: Write a two-column proof

  20. Have you learned. . . . • How to use the SSS Postulate to test for triangle congruence • How to use the SAS Postulate to test for triangle congruence • Assignment: • Non-Proof: Worksheet 4-4 • Proof: p.204(10-24Even, 30-47)

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