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CBSE Class 9 Answered

IN A PARALLELOGRAM ABCD THE BISECTORS OFANGLE A ALSO BISECTS BC AT X.PROVE THAT AD=2AB

Asked by M.s.srinidhi21 | 06 Oct, 2014, 07:02: AM
answered-by-expert Expert Answer
C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
G i v e n space t h a t space A X space i s space t h e space a n g l e space b i s e c t o r space o f space angle D A X T h u s comma space w e space h a v e comma angle D A X equals angle X A B.... left parenthesis 1 right parenthesis W e space h a v e comma space A D parallel to B C space a n d space A X E space i s space t h e space t r a n s v e r s a l. T h u s comma space sin c e space a l t e r n a t e space a n g l e s space a r e space e q u a l comma space w e space h a v e comma angle D A X equals angle A X B... left parenthesis 2 right parenthesis F r o m space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space h a v e comma angle X A B equals angle A X B C o n s i d e r space t h e space t r i a n g l e comma space triangle X A B : S i n c e space t h e space b a s e space a n g l e s comma space angle X A B space a n d space angle A X B space a r e space e q u a l comma space t h e space t r i a n g l e comma space triangle X A B space i s space a n space i s o c s e c l e s space t r i a n g l e T h u s comma space o p p o s i t e space s i d e s space a r e space e q u a l. rightwards double arrow A B equals X C B u t comma space A D equals 2 X C rightwards double arrow A D equals 2 A B
Answered by Vimala Ramamurthy | 06 Oct, 2014, 12:21: PM

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