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CBSE Class 9 Answered

ABCD is a parallelogram, in which X is the mid point of AB ,and Y is the mid point of CD. Prove that DXBY is a parallelogram.
 
Asked by Apoorv | 04 Aug, 2014, 10:55: AM
answered-by-expert Expert Answer
C o n s i d e r space t h e space g i v e n space d i a g r a m. S i n c e space X space i s space t h e space m i d p o i n t space o f space A B space w e space h a v e comma space A X equals X B S i m i l a r l y comma space sin c e space Y space i s space t h e space m i d p o i n t space o f space D C comma space w e space h a v e comma space D Y equals Y C A l s o comma space A B C D space i s space a space p a r a l l e log r a m space a n d space h e n c e comma space A B equals D C space a n d space A D equals B C T h e r e f o r e comma space X B equals D Y space a n d space A D equals B C A l s o comma space D X space a n d space B Y space a r e space t h e space t r n a s v e r s a l space l i n e s space a n d space A B space a n d space C D space a r e space p a r a l l e l space l i n e s space a n d space h e n c e comma space angle X D Y equals angle X B Y S i m i l a r l y comma space B X space a n d space D Y space a r e space t h e space t r a n s v e r s a l space l i n e s space a n d space A D space a n d space B C space a r e space p a r a l l e l space l i n e s space a n d space h e n c e comma space angle D X B equals angle B Y D T h u s comma space square D X B Y space i s space a l s o space a space p a r a l l e log r a m.
Answered by Vimala Ramamurthy | 05 Aug, 2014, 10:08: AM

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