Math, asked by abcdef15, 1 year ago

On three line segment OA ,OB and OC ate the point L,M,N respectively such that LM||AB and MN ||BC and A,B,Care non collinear points then prove that LN ||AC

Answers

Answered by grvbundela008p3f6id
5
tri OLM similar tri OAB

=> ang. O is common

ang OML = ang. OBA( LM//AB, CORESS. ANG.) (1)

=>ang OLM= ang OAB( LM//AB) (2)

OM/OB= OL/ OA= LM/AB (BY PRO. TH.) (3)

similarly tri OMN similar tri. OBC

OM/OB= ON/ OC= NM/CB (4)

FROM (3) N (4)

NM/CB= LM/ AB (5)

ang NML = ang OMN + ang OML= ang OBC +ang OBA (TRI ARE SIMILAR)

= ang CBA (6)

now tri NML and tri CBA

angNML = ang CBA(6)

NM/CB= LM/ AB (5)

tri are similar by S.A.S prop.f simiar tri

=>ang NLM= ang CAB (7)

SUB (7) FROM (2)

ang OLM - ang NLM =ang OAB - ang CAB

angOLN = ang OAC (CORESPONDING ANG ARE EQUAL)

LN// AC Q.E.D
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abcdef15: please send the figure
grvbundela008p3f6id: got it
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