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Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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In the following triangle, point O is the midpoint of LM, and point Pis the midpoint of LN. L. 2 of 5 Below is the proof that OP | MN. The proof is divided into four parts, where the title of each part indicates its main purpose. Complete part A of the proof. LM Part A: Prove 2 LO Statement Reason 1 LO = OM Definition of midpoint LM = LO+ Pick length v Segment addition postulate LM = LO+ Pick length v Substitution (1, 2) LM Pick value v Divide both sides by LO. (3) LO LO = OM Part A: Prove v Pick length LM = LO+ Pick length v LO Statement LM = LO+ v Pick length LO = OM LP 3. 1 LM 4 LO LP LM = LO+ PN Pic OP 3 LM = LO+ Pick length · OM LM Tart TIVT v Pick value LN Part B: Prove = 2 LP Stateme 1 [Show the steps.] 1 LO = 1/LO Part C: Prove ALMN ~ ALOP LM h v 2 [Show the steps.) LM 2/LO h v Part D: Prove OP || MN [Show the steps] LM 4 Pick value v LO
Transcribed Image Text:In the following triangle, point O is the midpoint of LM, and point Pis the midpoint of LN. L. 2 of 5 Below is the proof that OP | MN. The proof is divided into four parts, where the title of each part indicates its main purpose. Complete part A of the proof. LM Part A: Prove 2 LO Statement Reason 1 LO = OM Definition of midpoint LM = LO+ Pick length v Segment addition postulate LM = LO+ Pick length v Substitution (1, 2) LM Pick value v Divide both sides by LO. (3) LO LO = OM Part A: Prove v Pick length LM = LO+ Pick length v LO Statement LM = LO+ v Pick length LO = OM LP 3. 1 LM 4 LO LP LM = LO+ PN Pic OP 3 LM = LO+ Pick length · OM LM Tart TIVT v Pick value LN Part B: Prove = 2 LP Stateme 1 [Show the steps.] 1 LO = 1/LO Part C: Prove ALMN ~ ALOP LM h v 2 [Show the steps.) LM 2/LO h v Part D: Prove OP || MN [Show the steps] LM 4 Pick value v LO
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