5.5 Start Thinking. 5.5 Warm Up. 5.5 Cumulative Review Warm Up. Use a ruler to construct JKL with JK = 1 in., KL = 0.5 in.,

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1 5.5 tart hinking Use a ruler to construct JKL with JK = 1 in., KL = 0.5 in., JL = 1 in. What are the angle measurements in JKL? lassify JKL. onstruct a new triangle, PQ, with JK PQ, KL Q, JL P. re the angles congruent? Do you think it would be possible to create triangles with congruent side lengths but different angles? Why or why not? 5.5 Warm Up Name the included angle between the pair of sides given. 1. U and U 2. and 3. and 4. U and 5. and 6. and U 5.5 umulative eview Warm Up Find m 1 and m 2. ell which theorem you used esources by hapter 167

2 Name Date 5.5 Practice In Exercises 1 3, decide whether enough information is given to prove that the triangles are congruent using either the ongruence heorem (heorem 5.8) or the HL ongruence heorem (heorem 5.9). Explain Given: bisects D, D Prove: D D 5. Given: JL GF, KL HF, J and G are right angles. Prove: JKL GHF K F J G L H 6. he coordinates of two triangles are given by ( 2, 3 ), ( 1, 2 ), ( 4, 5) F( 2, 2 ), G( 4, 4 ), H( 4, 4 ). FGH. and Use the coordinates to determine whether 7. he figure shows a cut gem. a. What lengths can you measure to determine whether any two adjacent triangular faces of the gem are congruent? b. ssume that all of the triangular faces are congruent. What shape is the outline of the gem when viewed from above? 168 esources by hapter

3 Name Date 5.5 Practice In Exercises 1 3, decide whether enough information is given to prove that the triangles are congruent. If so, state the theorem you use Given: ED, FE, and D F Prove: D FE D E F 5. Given: P, Q P Prove: PQ Q P Q 6. wo triangles are formed by the four lines described below. oth triangles share lines a and b. side of one triangle is contained in line c, and a side of the other triangle is contained in line d. How can you use this information to determine whether the triangles are congruent? Line a: y = 3x + 2 Line b: y = 1x 1 3 Line c: passes through points ( 1, 5 ) and ( 3, 2) Line d: passes through points ( 6, 1 ) and ( 3, 7) esources by hapter 169

4 Name Date 5.5 Enrichment and Extension Proving riangle ongruence by solve for the missing variable. 1. If DEF, a. ( 1, 3, ) ( 4, 1, ) ( 5, 3, ) D( 3, 3, ) E( 6, 5, ) F( x, 3) b. ( 1, 1, ) ( 2, 2, ) ( 3, 4, ) D( 3, 3x 10, ) E( 6, 1, ) F( 7, 5) c. ( 3, 0, ) ( 6, 2, ) ( 1, 9, ) D( x 2 12, 10, ) E( 13, 8, ) F( 6, 1) In Exercises 2 and 3, use the diagram to write a two-column proof. 2. Given: W W ; is the midpoint of. Prove: 1 2 W Given: G G, Prove: G G G Q 4. Write a paragraph proof showing that if one side of an equilateral triangle is congruent to one side of a second equilateral triangle, then the two triangles are congruent. Include a diagram. Find the coordinates of J and K. 5. In the figure, MLN KLJ. y J L(e, f) K M(a, b) N(c, d) x 170 esources by hapter

5 Name Date 5.5 Puzzle ime What Did Mozart ecome On His hirteenth irthday? Write the letter of each answer in the box containing the exercise number. omplete the statement. 1. In a right triangle, the sides adjacent to the right angle are the. 2. he side opposite the right angle is the of the right triangle. 3. If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent according to the heorem. 4. If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent according to the heorem. olve for the indicated measure. 5. = 19, = 56, find m. 6. = 19, = 56, find m. 7. = 19, = 56, find m. olve. 8. rue or false? 9. re the two triangles congruent? ZXY Yes or no? nswers E. H. 65 E. legs.. yes diagonal. hypotenuse M.. arms G. true Y. no E. false. 56 X N. HL. 105 Z Y E esources by hapter 171