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ICSE Class 9 Answered

Prove that bisectors of any two adjacent angles of a parallelogram are at right angles
Asked by janhavipurswani | 21 Nov, 2018, 05:02: PM
answered-by-expert Expert Answer
In the figure, Let ABCD is a paralellogram.
 
begin mathsize 12px style angle end styleDAB  + begin mathsize 12px style angle end styleCBA  = 180° ......................(1)
 
begin mathsize 12px style angle end styleOAB = (1/2)begin mathsize 12px style angle end styleDAB ......................(2)
begin mathsize 12px style angle end styleOBA = (1/2)begin mathsize 12px style angle end styleCBA ......................(3)
by adding (2) and (3) and using eqn.(1) ,   begin mathsize 12px style angle end styleOAB + begin mathsize 12px style angle end styleOBA = (1/2) ( begin mathsize 12px style angle end styleDAB + begin mathsize 12px style angle end styleCBA ) = 90°
Hence begin mathsize 12px style angle end styleAOB = 180-(  begin mathsize 12px style angle end styleOAB + begin mathsize 12px style angle end styleOBA ) = 90°
Answered by Thiyagarajan K | 22 Nov, 2018, 04:24: AM

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