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Warm Up

Prove Triangles Congruent by SSS. Warm Up. Lesson Presentation. Lesson Quiz. 1. Write a congruence statement. P. M. R. Q. N. O. ANSWER. ∆ MNO ∆PRQ. Warm-Up. 2. How do you know that N R ?. P. M. R. Q. N. O. ANSWER. Third s Thm. Warm-Up. 3. Find x.

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Warm Up

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  1. Prove Triangles Congruent by SSS Warm Up Lesson Presentation Lesson Quiz

  2. 1. Write a congruence statement. P M R Q N O ANSWER ∆MNO ∆PRQ Warm-Up

  3. 2. How do you know that N R? P M R Q N O ANSWER Third s Thm. Warm-Up

  4. 3.Find x. (3x)º (2x + 10)º (7x – 50)º ANSWER 30 Warm-Up

  5. 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 Write a proof.

  6. DFGHJK ANSWER yes; SSS Guided Practice Decide whether the congruence statement is true. Explain your reasoning.

  7. ACBCAD 2. ANSWER No; corresponding sides AB and CD are not congruent. Guided Practice Decide whether the congruence statement is true. Explain your reasoning.

  8. 3. QPTRST ANSWER yes; SSS Guided Practice Decide whether the congruence statement is true. Explain your reasoning.

  9. 2 2 ( – ( ) ) – 1 ) (– 5 1 – 4 PR + = 2 2 = 5 ) (– 3 25 4 = + = 2 – ( ) + 2 – ( ) y y x x 1 2 2 1 d = Example 2 SOLUTION By counting, PQ = 4 and QR = 3. Use the Distance Formula to find PR.

  10. By the SSS Congruence Postulate, any triangle with side lengths 3, 4, and 5 will be congruent to PQR. ANSWER The correct answer is A. 2 2 2 2 = (–4) – (–1) ( ( 5 – 1) ) 5 ) (– 3 25 4 = + = + Example 2 The distance from (–1, 1) to (–1, 5) is 4. The distance from (–1, 5) to (–4, 5) is 3. The distance from (– 1, 1) to (–4, 5) is

  11. has vertices J(–3, –2), K(0, –2), and L(–3, –8). RSThas vertices R(10, 0), S(10, – 3), and T(4, 0). Graph the triangles in the same coordinate plane and show that they are congruent. 4. JKL ANSWER KJ = SR =3, JL = RT =6, LK = TS =3 5 Guided Practice

  12. Structural Support Explain why the bench with the diagonal support is stable, while the one without the support can collapse. Example 3

  13. 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. Example 3

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

  15. ANSWER The diagonal support forms triangle with fixed side length by SSS congruence postulate, these triangles can not change shape. The figure is stable. Guided Practice Determine whether the figure is stable. Explain your reasoning.

  16. 7. ANSWER The diagonal support is not stable because the lower half of figure dies not have diagonal support. Guided Practice Determine whether the figure is stable. Explain your reasoning.

  17. 1. The vertices GHI and RST are G(–2, 5), H(2, 5),I(–2, 2), R(–9, 8), S(–5, 8), and T(–9, 5). Is GHI RST? Explain. ANSWER Yes.GH = RS = 4, HI = ST = 5, andIG = TR = 3. By the SSS post ., it followsthatGHI RST. Lesson Quiz

  18. 2. Is ABC XYZ? Explain. ANSWER Yes. By the Seg. Add. Post.,AC XZ. Also ,AB XY and BC YZ. So ABC XYZby theSSS Post. Lesson Quiz

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