WarmUp Exercises 1 Write a congruence statement P

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

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

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

Warm-Up 1 Exercises EXAMPLE Use the SSS Congruence Postulate Write a proof. GIVEN PROVE Proof KL NL, KM KLM NM NLM It is given that KL NL and KM By the Reflexive Property, LM So, by the SSS Congruence Postulate, KLM NM LN.

Warm-Up Exercises GUIDED PRACTICE for Example 1 Decide whether the congruence statement is true. Explain your reasoning. 1. DFG HJK SOLUTION Three sides of one triangle are congruent to three sides of second triangle then the two triangle are congruent. Side DG HK, Side DF JH, and Side FG So by the SSS Congruence postulate, Yes. The statement is true. JK. DFG HJK.

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

Warm-Up Exercises GUIDED PRACTICE for Example 1 Therefore the given statement is false and ABC is not Congruent to CAD because corresponding sides are not congruent

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

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

Warm-Up 2 Exercises EXAMPLE Standardized Test Practice PR = = ( – 1 – (– 5 ) )2 + ( 1 – 4 ) 2 4 2 + (– 3 ) 2 = 25 = 5 By the SSS Congruence Postulate, any triangle with side lengths 3, 4, and 5 will be congruent to PQR. 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 ( 5 – 1) 2 + ( (– 4) – (– 1) ) 2 = 4 2 + (– 3 ) 2 = ANSWER The correct answer is A. 25 = 5

Warm-Up Exercises GUIDED PRACTICE 4. for Example 2 JKL has vertices J(– 3, – 2), K(0, – 2), and L(– 3, – 8). RST has 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. ANSWER KJ = SR = 3. JL = RT = 6. LK = TS = 3 5.

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

Warm-Up 3 Exercises EXAMPLE Solve a real-world problem 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.

Warm-Up Exercises GUIDED PRACTICE for Example 3 Determine whether the figure is stable. Explain your reasoning. 5. SOLUTION The figure is without a diagonal support is not stable Because there are many possible quadrilaterals with the given side lengths.

Warm-Up Exercises GUIDED PRACTICE for Example 3 Determine whether the figure is stable. Explain your reasoning. 6. SOLUTION The diagonal support forms triangle with fixed side length by SSS congruence postulate, these triangles can not change shape. The figure is stable.

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

Daily Homework Quiz Warm-Up Exercises 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, and IG = TR = 3. By the SSS post. , it follows that GHI RST.

Daily Homework Quiz Warm-Up Exercises 2. Is ABC ANSWER XYZ? Explain. Yes. By the seg. Add. Post. , AC XZ. Also , AB XY and BC YZ. So ABC XYZ by the SSS post.