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CBSE Class 9 Answered

ABCD is square. E is midpoint of BC. F is a point on side CD. join E and F. AR bisect the side R. Then prove that the F is mid point of side BC.
Asked by education.bps | 19 Oct, 2015, 01:42: PM
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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.
E space i s space m i d p o i n t space o f space B C space a n d space F space i s space t h e space m i d p o i n t space o f space C D. G i v e n space t h a t space A C space b i s e c t s space E F. space left parenthesis Q u e s t i o n space s t a t e m e n t space i s space i n c o r r e c t. space P l e a s e space C h e c k 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 triangle C E F. T h u s comma space triangle C E F space i s space a space r i g h t space t r i a n g l e space a n d space angle E G C equals angle F G C equals 90 degree... 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 s space triangle E G C space a n d space triangle F G C E G equals G F space space space space open parentheses A C space b i s e c t s space t h e space s i d e space E F close parentheses angle E G C equals angle F G C equals 90 degree space space space space open parentheses f r o m space e q u a t i o n space left parenthesis 1 right parenthesis close parentheses G C equals G C space space space space space open parentheses c o m m o n close parentheses T h u s comma space b y space S i d e minus A n g l e minus S i d e space c r i t e r i o n space o f space c o n g r u e n c e comma space w e space h a v e comma triangle E G C approximately equal to triangle F G C C o r r e p o n d i n g space p a r t s space o f space t h e space c o n g r u e n t space t r i a n g l e s space a r e space c o n g r u e n t. H e n c e comma space C F equals E C space a n d space A B C D space i s space a space s q u a r e. T h u s comma space F space i s space t h e space m i d p o i n t space o f space B C.
Answered by Vimala Ramamurthy | 20 Oct, 2015, 06:16: PM

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