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CBSE Class 9 Answered

L and M are the midpoints of the diagonals BD and AC respectively of the quadrilateral ABCD. Through D, draw DE equal and parallel to AB. Show that EC is parallel to LM and is double of it

Asked by Paresh | 10 Dec, 2015, 10:19: 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.
A B C D space i s space a space q u a d r i l a t e r a l. space M space i s space t h e space m i d p o i n t space o f space t h e space d i a g o n a l space A C space a n d space L space i s space t h e space m i d p o i n t space o f space t h e d i a g o n a l space B D. D E space i s space d r a w n space p a r a l l e l space t o space A B space a n d space D E equals A B T h e r e f o r e comma space A B E D space i s space a space p a r a l l e log r a m. I n space a space p a r a l l e log r a m comma space d i a g o n a l s space b i s e c t space e a c h space o t h e r. T h u s space A E space p a s s e s space t h r o u g h space t h e space m i d p o i n t space o f space B D. H e n c e space A E space p a s s e s space t h r o u g h space L. S o comma space D i a g o n a l s space A E space a n d space B D space b i s e c t space e a c h space o t h e r. T h a t space i s comma space L space i s space t h e space m i d p o i n t space o f space A E. W e space a l s o space h a v e comma space M space i s space t h e space m i d p o i n t space o f space A C. J o i n space E C. N o w space c o n s i d e r space t h e space t r i a n g l e comma space A C E L space i s space t h e space m i d p o i n t space o f space A E space a n d space M space i s space t h e space m i d p o i n t space o f space A C. T h u s space b y space m i d p o i n t space t h e o r e m comma space w e space h a v e comma space L M space i s space p a r a l l e l space t o space t h e space t h i r d space s i d e space A C a n d space i s space e q u a l space t o space 1 half A C L M equals 1 half A C rightwards double arrow A C equals 2 L M H e n c e space p r o v e d. space
Answered by Vimala Ramamurthy | 10 Dec, 2015, 11:51: AM
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