Name Class Date. Given ABCD QRST, find corresponding parts using the names. Order matters.

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1 Name lass ate Reteaching ongruent igures RS, find corresponding parts using the names. Order matters. or example, RS or example, RS his shows that corresponds to. herefore,. his shows that corresponds to RS. herefore, RS. xercises ind corresponding parts using the order of the letters in the names. 1. Identify the remaining three pairs of corresponding angles and sides between and RS using the circle technique shown above. ngles: Sides: RS RS RS RS RS RS 2. Which pair of corresponding sides is hardest to identify using this technique? nswers may vary. Sample: and ind corresponding parts by redrawing figures. 3. he two congruent figures below at the left have been redrawn at the right. Why are the corresponding parts easier to identify in the drawing at the right? K K nswers may vary. Sample: he drawing at the right shows figures in same orientation. 4. Redraw the congruent polygons at the right in the same orientation. Identify all pairs of corresponding sides and angles. heck students work. j and j, j and j, j and jr, j and js, j and j, and, and R, and RS, and S, and and all correspond. S R 5. MNO RS. Identify all pairs of congruent M N R S sides and angles. O jm@j, jn@jr, jo@js, j@j, MN@R, NO@RS, O@S, and M@ opyright by earson ducation, Inc., or its affiliates. ll Rights Reserved.

2 Name lass ate Reteaching (continued) ongruent igures roblem, m = 30, and m = 65, what is m? ow might you solve this problem? Sketch both triangles, and put all the information on both diagrams m = 30; therefore, m = 30. ow do you know? ecause and are corresponding parts of congruent triangles. 30 xercises Work through the exercises below to solve the problem above. 6. What angle in has the same measure as? What is the measure of that angle? dd the information to your sketch of. j; ou know the measures of two angles in. ow can you find the measure of the third angle? nswers may vary. Sample: Use riangle ngle-sum hm. Set sum of all three angles equal to What is m? ow did you find your answer? 85; answers may vary. Sample: mj = 180 ( ) efore writing a proof, add the information implied by each given statement to your sketch. hen use your sketch to help you with xercises dd the information implied by each given statement. 9. : and are right angles. mj = mj = 90, # and # 10. : and. is a parallelogram because it has opposite sides that are congruent. 11. :. } 12. an you conclude that using the given information above? If so, how? es; use the hird ngles hm. 13. ow can you conclude that the third side of both triangles is congruent? he third side is shared by both triangles and is congruent by the Refl. rop. of ongruence. opyright by earson ducation, Inc., or its affiliates. ll Rights Reserved.

3 Name lass ate Reteaching riangle ongruence by SSS and SS ou can prove that triangles are congruent using the two postulates below. ostulate 4-1: Side-Side-Side (SSS) ostulate If all three sides of a triangle are congruent to all three sides of another triangle, then those two triangles are congruent. J K If JK, KL, and JL, then JKL. In a triangle, the angle formed by any two sides is called the included angle for those sides. L ostulate 4-2: Side-ngle-Side (SS) ostulate If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then those two triangles are congruent. R If, R, and, then R. is included by and R. is included by and. xercises 1. What other information do you need to prove R R by SS? by the Reflexive roperty of ongruence, R@R. It is given that jr@jr. hese are the included angles for the corresponding congruent sides. R 2. What other information do you need to prove by SS? xplain. j@j; hese are the included angles between the corresponding congruent sides. 3. eveloping roof opy and complete the flow proof. : M, J rove: J M J M J J M SS Vertical are. jm opyright by earson ducation, Inc., or its affiliates. ll Rights Reserved.

4 Name lass ate Reteaching (continued) riangle ongruence by SSS and SS Would you use SSS or SS to prove the triangles congruent? If there is not enough information to prove the triangles congruent by SSS or SS, write not enough information. xplain your answer J 6. M M Not enough information; two pairs of corresponding Not enough Not enough information; only sides are congruent, but the information; you two pairs of corresponding congruent angles are not the need to know if sides are congruent. ou need included to know or j@j. 7. : O SO, O is the 8. : I, #I midpoint of N. rove: NO OS N O Statements: 1) O@SO; 2) O is the midpoint of N; 3) NO@O; 4) jno@jos; 5) NO@ OS; Reasons: 1) ; 2) ; 3) ef. of midpoint; 4) Vert. are@; 5) SS S rove: I 9. carpenter is building a support for a bird feeder. e wants the triangles on either side of the vertical post to be congruent. e measures and finds that and that. What would he need to measure to prove that the triangles are congruent using SS? What would he need to measure to prove that they are congruent using SSS? Statements: 2) I@, #I; 3) j and ji are rt. ; 4) j@ji; 5) I@ ; Reasons: 1) Refl. rop.; 2) ; 3) ef. of perpendicular; 4) ll rt. are@; 5) SS I or SS, he would need to determine if j@j; for SSS, he would need to determine 10. n artist is drawing two triangles. She draws each so that two sides are 4 in. and 5 in. long and an angle is 55. re her triangles congruent? xplain. nswers may vary. Sample: Maybe; if both the 55 angles are between the 4-in. and 5-in. sides, then the triangles are congruent by SS. opyright by earson ducation, Inc., or its affiliates. ll Rights Reserved.

5 Name lass ate Reteaching riangle ongruence by S and S roblem an the S ostulate or the S heorem be applied directly to prove the triangles congruent? R a. ecause R and are right angles, they are congruent. by the Reflexive roperty of, and it is given that R. herefore, R by the S heorem. xercises Indicate congruences. 1. opy the top figure at the right. Mark the figure with the angle congruence and side congruence symbols that you would need to prove the triangles congruent by the S ostulate. 2. opy the second figure shown. Mark the figure with the angle congruence and side congruence symbols that you would need to prove the triangles congruent by the S heorem. b. It is given that and. ecause and are vertical angles, they are congruent. herefore, by the S ostulate. 3. raw and mark two triangles that are congruent by either the S ostulate or the S heorem. heck students work. What additional information would you need to prove each pair of triangles congruent by the stated postulate or theorem? S ostulate 5. S heorem J K 6. S ostulate j@j jjmk@jlkm, j@jvu jjkm@jlmk, jjmk@jlmk, or jjkm@jlkm M L 7. S heorem 8. S heorem 9. S ostulate j@jo O j@j R jl@jl U V L opyright by earson ducation, Inc., or its affiliates. ll Rights Reserved.

6 Name lass ate Reteaching (continued) riangle ongruence by S and S 10. rovide the reason for each step in the two-column proof. : } VW, U VU, U WVU, UWV is a right angle. rove: U VUW Statements 1) UWV is a right angle. 2) VW#W 3) } VW 4) #W 5) U is a right angle. 6) UWV U 7) U VU 8) U WVU 9) U VUW 1)? 2)? 3)? 4)? 5)? 6)? 7)? 8)? 9)? Reasons efinition of perpendicular lines erpendicular ransversal heorem efinition of perpendicular lines ll right angles are congruent. S heorem U V W 11. Write a paragraph proof. : W } ; W } rove: W W W It is given that W} and W}, so jw@jw and jw@jw, by the lternate Interior hm. W@W by the Reflexive roperty of@. So, by S ost. W@ W. 12. eveloping roof omplete the proof by filling in the blanks. :, 1 2 rove: 4 roof: and 1 2 are given. by? 2. Refl. rop. of ongruence So, by?. S Write a paragraph proof. 1 6 : 1 6, 3 4, L O 2 5 rove: LM ON L M 4 N O 3 j3@j4 is given. herefore, mj3 = mj4, by def. of@js. ecause j2 and j3 are linear pairs, and j4 and j5 are linear pairs, the pairs of angles are suppl. herefore, j2@j5 by the ongruent Suppl. hm. j1@j6 and L@O are given, so LM@ ON, by the S hm. opyright by earson ducation, Inc., or its affiliates. ll Rights Reserved.