In triangle ABC, D and E are midpoints of side AB and AC respectively. Also, DE is parallel to BC. Prove that ABC is an isosceles triangle. (4 marks )

Asked by Anukruti Valase | 7th Aug, 2014, 10:32: PM

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Q: In triangle ABC, D and E are the midpoints of sides AB and AC respectively. Also DE is parallel to BC and BD = CE. Prove that ABC is an isoceles triangle. [CBSE 2007 & 2009].
 
G i v e n : space I n space increment A B C comma space D space a n d space E space a r e space m i d p o i n t s space o f space A B space a n d space A C space r e s p e c t i v e l y. space A l s o space D E parallel to thin space B C space a n d space B D space equals space C E.  T o space P r o v e : space A B space equals space A C  P r o o f : space I n space increment A B C comma space D space a n d space E space a r e space m i d p o i n t s space o f space A B space a n d space A C space r e s p e c t i v e l y space a n d space D E parallel to space B C. space T h e n comma space b y space B a s i c space P r o p o r t i o n a l i t y space t h m. comma  fraction numerator A D over denominator B D end fraction space equals space fraction numerator A E over denominator E C end fraction space space space space space  fraction numerator A D space plus space D B over denominator B D end fraction space equals space fraction numerator A E space plus space E C over denominator E C end fraction fraction numerator A B over denominator B D end fraction equals fraction numerator A C over denominator E C end fraction space space space space space space space minus minus minus minus minus minus left parenthesis i right parenthesis  N o w comma space g i v e n space i s space B D space equals space E C comma space t h e n space u sin g space i t space i n space left parenthesis i right parenthesis space w e space g e t comma  fraction numerator A B over denominator B D end fraction equals fraction numerator A C over denominator B D end fraction space space T h e n comma space A B space equals space A C.  F o r space increment A B C comma space i f space A B space equals space A C space t h e n space i t space i s space a n space i s o c e l e s space a n space t r i a n g l e comma

Answered by Mili Hariyani | 8th Aug, 2014, 03:08: PM

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