if E is any mid point on median AD of a triangle ABC.show that area (ABE)=area (ACE).

Asked by paddipawar | 26th Nov, 2014, 06:26: AM

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 space i s space a space t r i a n g l e space a n d space A D space i s space t h e space m e d i a n space o f space t h e space t r i a n g l e space m e e t s space B C space i n space D. S i n c e space t h e space m e d i a n space d i v i d e s space t h e space t r i a n g l e space i n t o space e q u a l space a r e a s space o f space t w o space t r i a n g l e s comma space w e space h a v e comma A r e a open parentheses triangle A B D close parentheses equals A r e a open parentheses triangle A C D close parentheses... left parenthesis 1 right parenthesis 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 space B C E. S i n c e space A D space i s space t h e space m e d i a n comma space E D space i s space a l s space t h e space m e d i a n space o f space t h e space t r i a n g l e space B C E. T h e r e f o r e comma space w e space h a v e comma A r e a open parentheses triangle B E D close parentheses equals A r e a open parentheses triangle C E D close parentheses... left parenthesis 2 right parenthesis S u b t r a c t i n g space e q u a t i o n space left parenthesis 2 right parenthesis space f r o m space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma A r e a open parentheses triangle A B D close parentheses minus A r e a open parentheses triangle B E D close parentheses equals A r e a open parentheses triangle A C D close parentheses minus A r e a open parentheses triangle C E D close parentheses rightwards double arrow A r e a open parentheses triangle A B E close parentheses equals A r e a open parentheses triangle A C E close parentheses H e n c e space p r o v e d.

Answered by Vimala Ramamurthy | 26th Nov, 2014, 09:47: AM

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