Given: ABCD is a rhombus.Prove AC BD Given: ABCD is a rhombusProve: AC 1 BDDABCD is a rhombus. We know that AB= BC byABCD is a parallelogram and we know that AP=PC becausePB= PB|by. So, AAPB = ACPB by. ZAPB = LCPB by. ZAPB = LCPB also form a linear pair and are supplementary. If two congruent angles aresupplementary, they must each measure 90°. Therefore, LAPB_is a right angle byand AC I BD by

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Description: Given: ABCD is a rhombus.Prove AC BD Given: ABCD is a rhombusProve: AC 1 BDDABCD is a rhombus. We know that AB= BC byABCD is a parallelogram and we know that AP=PC becausePB= PB|by. So, AAPB = ACPB by. ZAPB = LCPB by. ZAPB = LCPB also form a linear p

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Given: ABCD is a rhombus B Prove: AC 1 BD P D ABCD is a rhombus. We know that ABE BC by ABCD is a parallelogram and we know that |AP = PC because PB= PB by So, ДАРВ — ДСРВ by

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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Given: ABCD is a rhombus.
Prove AC BD

Given: ABCD is a rhombus
Prove: AC 1 BD
D
ABCD is a rhombus. We know that AB= BC by
ABCD is a parallelogram and we know that AP=PC because
PB= PB|by
. So, AAPB = ACPB by
. ZAPB = LCPB by
. ZAPB = LCPB also form a linear pair and are supplementary. If two congruent angles are
supplementary, they must each measure 90°. Therefore, LAPB_is a right angle by
and AC I BD by

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