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CBSE Class 9 Answered

Prove the line segment joining the mid points of the diagonal of trapezium is parallel to each of the parallel sides.

Asked by M.s.srinidhi21 | 06 Oct, 2014, 06:47: AM
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begin mathsize 14px style G i v e n ; space A B C D space i s space a space t r a p e z i u m space w i t h space A B parallel to C D space a n d space A C space a n d space B D space a r e space t h e space d i a g o a n a l s. space P space i s space t h e space m i d p o i n t space o f space A C space a n d space Q space b e space t h e space m i d p o i n t space o f space B D. T o space P r o v e : space P Q parallel to A B space a n d space P Q parallel to C D P r o o f : space A B space vertical line vertical line space C D space a n d space t r a n s v e r s a l space A C space c u t s space t h e m space a t space A space a n d space C space r e s p e c t i v e l y. therefore angle 3 space approximately equal to space angle 4 space left parenthesis A l t e r n a t e space a n g l e s right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space...... space left parenthesis i right parenthesis space C o n s t r u c t space stack D R with bar on top space s u c t space t h a t space R space l i e s space o n space A B space a n d space P space i s space t h e space m i d p o i n t space o f space D R. N o w comma space I n space capital delta A P R space a n d space capital delta D P C comma space angle 3 space approximately equal to space angle 4 space space space space space space space space space space space left parenthesis b y space left parenthesis i right parenthesis right parenthesis space stack A P with bar on top space approximately equal to space stack C P with bar on top space space space space space space space space space space space space left parenthesis P space i s space m i d p o i n t space o f space A C right parenthesis space angle 1 space approximately equal to space angle 2 space space space space space space space space space space space space left parenthesis V e r t i c a l l y space o p p o s i t e space a n g l e s right parenthesis space therefore space capital delta A P R space approximately equal to space space capital delta D P C space T h e n space w e space g e t space stack A R with bar on top space approximately equal to space stack D C with bar on top space a n d space stack P R with bar on top space approximately equal to space stack D P with bar on top space I n space capital delta D R B comma space P space a n d space Q space a r e space t h e space m i d p o i n t s space o f space s i d e s space D R space a n d space D B space r e s p e c t i v e l y. space therefore space P Q space vertical line vertical line space B R space therefore space P Q space vertical line vertical line space A B space therefore space P Q space vertical line vertical line space A B space a n d space P Q space parallel to space C D end style

Answered by Mili Hariyani | 06 Oct, 2014, 11:11: AM

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