IF PQRS IS A PARALLELOGRAM,PQ AND QO ARE,RESPECTIVELY THE ANGLE BISECTS OF ANGLE P AND ANGLE Q.LINE LOM IS DRAWN PARALLEL TO PQ.PROVE THAT

1. PL=QM

2. LO=OM

Asked by M.s.srinidhi21 | 6th Oct, 2014, 06:57: AM

Expert Answer:

G i v e n : space I n space square m P Q R S comma space P O space a n d space Q O space a r e space t h e space a n g l e space b i s e c t o r s space o f space P space a n d space Q space r e s p e c t i v e l y space w h i c h space i n t e r s e c t space a t space O. space A l s o space L O M space i s space a space l i n e space p a s sin g space t h r o u g h space O space s u c h space t h a t space L space l i e s space o n space P S space a n d space M space l i e s space o n space Q R.  T o space p r o v e : space i right parenthesis space P L space parallel to space Q M space space space i i right parenthesis space L O space equals space O M

begin mathsize 14px style P r o o f : i right parenthesis space space I n space square m space P Q R S comma space P S space parallel to space Q R space t h e n space P L space parallel to space Q R space therefore space P L space parallel to space Q M space space space space space space space left parenthesis a s space M space l i e s space o n space Q R right parenthesis a n d space P Q space parallel to space L M space space left parenthesis g i v e n right parenthesis therefore space square P Q L M space i s space a space p a r a l l e log r a m. therefore space P L space equals space Q M  i i right parenthesis space N o w comma space angle L P O space equals space angle O P Q space space space left parenthesis stack O P space with rightwards arrow on top i s space t h e space a n g l e space b i s e c t o r right parenthesis B u t space angle L O P space equals space angle O P Q space space space space space space space space left parenthesis a l t e r n a t e space a n g l e s right parenthesis therefore space angle L O P space equals space angle L P O therefore space P L space equals space L O  S i m i l a r l y space w e space c a n space g e t space Q M space equals space M O B u t space b y space i right parenthesis space w e space h a v e space p r o v e d space t h a t space P L space equals space Q M space t h e n space L O space equals space O M end style


Answered by Mili Hariyani | 6th Oct, 2014, 11:56: AM