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Congruence Statements and Proofs

Learn about congruence statements and proofs using the SSS Congruence Postulate. Practice solving real-world problems.

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Congruence Statements and Proofs

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

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

  3. 3.Find x. (3x)º (2x + 10)º (7x – 50)º ANSWER 30

  4. Write a proof. 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 Use the SSS Congruence Postulate

  5. DFGHJK SideDG HK, SideDF JH,andSideFG JK. So by the SSS Congruence postulate, DFG HJK. for Example 1 GUIDED PRACTICE Decide whether the congruence statement is true. Explain your reasoning. SOLUTION Three sides of one triangle are congruent to three sides of second triangle then the two triangle are congruent. Yes. The statement is true.

  6. ACBCAD 2. GIVEN : BC AD ACBCAD PROVE : It is given that BC AD By Reflexive property AC AC, But AB is not congruent CD. PROOF: for Example 1 GUIDED PRACTICE Decide whether the congruence statement is true. Explain your reasoning. SOLUTION

  7. for Example 1 GUIDED PRACTICE Therefore the given statement is false and ABC is not Congruent to CAD because corresponding sides are not congruent

  8. 3. QPTRST GIVEN : QT TR , PQ SR, PT TS PROVE : QPTRST It is given that QT TR, PQ SR, PT TS.So by SSS congruence postulate, QPT RST. Yes the statement is true. PROOF: for Example 1 GUIDED PRACTICE Decide whether the congruence statement is true. Explain your reasoning. SOLUTION

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

  10. 2 2 ( – ( ) ) – 1 ) (– 5 1 – 4 PR + = 2 2 = 5 ) (– 3 25 4 = + = By the SSS Congruence Postulate, any triangle with side lengths 3, 4, and 5 will be congruent to PQR. 2 2 2 2 = (–4) – (–1) ( ( 5 – 1) ) 5 ) (– 3 25 4 = + = + The correct answer is A. ANSWER EXAMPLE 2 Standardized Test Practice 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. ANSWER KJ = SR =3. JL = RT =6. LK = TS =3 5. for Example 2 GUIDED PRACTICE 4. 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. JKL

  12. Structural Support Explain why the bench with the diagonal support is stable, while the one without the support can collapse. EXAMPLE 3 Solve a real-world problem

  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 Solve a real-world problem

  14. for Example 3 GUIDED PRACTICE 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.

  15. for Example 3 GUIDED PRACTICE Determine whether the figure is stable. Explain your reasoning. SOLUTION The diagonal support forms triangle with fixed side length by SSS congruence postulate, these triangles can not change shape. The figure is stable.

  16. 7. for Example 3 GUIDED PRACTICE Determine whether the figure is stable. Explain your reasoning. SOLUTION The diagonal support is not stable because the lower half of figure dies not have diagonal support.

  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. Daily Homework 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. Daily Homework Quiz

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