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Name _______________________________________ Date __________________ Class __________________ LESSON 4-6 Practice B Triangle Congruence: CPCTC 1. Heike Dreschler set the Woman’s World Junior Record for the long jump in 1983. She jumped about 23.4 feet. The diagram shows two triangles and a pond. Explain whether Heike could have jumped the pond along path BA or along path CA. ________________________________________________________________________________________ ________________________________________________________________________________________ ________________________________________________________________________________________ ________________________________________________________________________________________ Reflexive Property ASA CPCTC Given KM KM KJ || LM LKM JMK Parallel lines cut by a transversal form congruent alt. int. angles. Write a proof. 2. Given: L J, KJ || LM Prove: LKM JMK Statement Reason 1.) 2.) 2.) Given 3.) 4.) 4.) 5.) 6.) 6.) Name _______________________________________ Date __________________ Class __________________ 7. 3; 5 ; 4 ; 3 ; 5 ; 4 8. SSS have equal lengths, so the diagonals bisect each other. 9. CPCTC 2. Possible answer: From the definition of a rhombus, IH is congruent to FG , IF is congruent to GH , and IH is parallel to FG . By Alternate Interior Angles Theorem, GFH is congruent to IHF and FGI is congruent to HIG. Therefore FGJ is congruent to HIJ by ASA. By CPCTC, FJ is congruent to HJ and GJ is congruent to IJ . So FJI is congruent to GHJ by SSS. But HIJ is also congruent to FIJ by SSS. And so all four triangles are congruent by the Transitive Property of Congruence. By CPCTC and the Segment Addition Postulate, FH is congruent to GI . By CPCTC and the Linear Pair Theorem, FJI, GJF, HJG, and IJH are right angles. So FH and GI are perpendicular. By CPCTC, GFH, IFH, GHF, and IHF are congruent, so FH bisects IFG and IHG. Similar reasoning shows that GI bisects FGH and FIH. Practice B 1. Possible answer: Because DCE BCA by the Vertical s Thm. the triangles are congruent by ASA, and each side in ABC has the same length as its corresponding side in EDC. Heike could jump about 23 ft. The distance along path BA is 20 ft because BA corresponds with DE, so Heike could have jumped this distance. The distance along path CA is 25 ft because CA corresponds with CE, so Heike could not have jumped this distance. 2. 3. Statements Reasons 1. FGHI is a rectangle. 1. Given 2. FI GH, FIH and GHI are right angles. 2. Def. of rectangle 3. FIH GHI 3. Rt. Thm. 4. IH IH 4. Reflex. Prop. of 4. The diagonals of a square are congruent perpendicular bisectors that bisect the vertex angles of the square. 5. FIH GHI 5. SAS 5. The diagonals are congruent. 6. FH GI 6. CPCTC 7. FH GI 7. Def. of segs. 3. The diagonals of a rectangle bisect each other. Reteach 1. Practice C 1. Possible answer: From the definition of a parallelogram, DC is congruent to AB and DC is parallel to AB . By the Alternate Interior Angles Theorem, BAC is congruent to DCA and CDB is congruent to ABD. Therefore ABE is congruent to CDE by ASA. By CPCTC, DE is congruent to BE and AE is congruent to CE . Congruent segments 2. Statements Reasons 1. UXW and UVW are rt. s. 1. Given 2. UX UV 2. a. Given Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. A38 Holt Geometry Name _______________________________________ Date __________________ Class __________________