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4.3  Prove Triangles Congruent by SSS

4.3  Prove Triangles Congruent by SSS. SSS. Statements. reasons. Use the given coordinates to determine if. B. A. C. D. F. E. Structural Support. Explain why the bench with the diagonal support is stable, while the one without the support can collapse. SOLUTION.

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4.3  Prove Triangles Congruent by SSS

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  1. 4.3  Prove Triangles Congruent by SSS

  2. SSS

  3. Statements reasons

  4. Use the given coordinates to determine if B A C D F E

  5. Structural Support Explain why the bench with the diagonal support is stable, while the one without the support can collapse.

  6. SOLUTION The bench with a diagonal support forms triangles with fixed side lengths. By the SSS Congruence Postulate, these triangles cannot change shape, so the bench is stable. The bench without a diagonal support is not stable because there are many possible quadrilaterals with the given side lengths.

  7. Determine whether the figure is stable. Explain your reasoning. SOLUTION The figure is without a diagonal support is not stable Because there are many possible quadrilaterals with the given side lengths.

  8. SOLUTION The diagonal support forms triangle with fixed side length by SSS congruence postulate, these triangles can not change shape. The figure is stable.

  9. 7. SOLUTION

  10. Homework:A#31pg. 236 #1 - 10, 13 - 21 24 and 26

  11. 4.4 Prove Triangles Congruent by SAS and HL

  12. Postulate 20: Side-Angle-Side (SAS) Congruence Postulate • If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

  13. Not enough The angle must be between the two congruent sides!

  14. SSS

  15. SAS

  16. SAS

  17. Reasons Statements 1. Given 1.

  18. Statements Reasons Given 1. 3 1 2 4

  19. Theorem 4.5: Hypotenuse-Leg (HL) Congruence Theorem • If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent.

  20. Prove the triangles are congruent, or state that not enough information is given. HL

  21. Is enough information given to prove the triangles congruent? Yes; HL

  22. WY XZ,WZ ZY, XY ZY WYZXZY PROVE EXAMPLE 3 Reasons Statements Given 1.

  23. Assignment #32Page 243#3-15, 25-27, 34-38

  24. Homework Day 5Page 236 #1-8, 10, 13-19, 24 and 26Page 246 #35 - 38

  25. Homework Day 5 (cont’d) Page 236 # 1 -8, 10, 13 – 19, 24, 26 Page 246 #35 - 38

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