WarmUp 1 Exercises EXAMPLE Use the SSS Congruence
- Slides: 8
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.
