ABCD is a square. E and F are pints os sides BC and CD respectively such that EF is parallel to diagonal BD. AM is perpendicular to EF. Show that ar(AEM)=ar(AMF)

Asked by bis0584 | 2nd Mar, 2015, 01:03: PM

Expert Answer:

$D i a g o n a l space A C space b i s e c t s space D i a g o n a l space B D space a t space r i g h t space a n g l e s. D O equals O B space left square bracket S i n c e space A B C D thin space i s space a space s q u a r e right square bracket I n space increment C F E space a n d space increment space C D B comma angle C F E equals angle C D B space left square bracket C o r r e s p o n d i n g space a n g l e s right square bracket angle F C E equals angle B D C space left square bracket C o m m o n space A n g l e right square bracket increment C F E tilde increment space C D B space left square bracket A A right square bracket fraction numerator C F over denominator C D end fraction equals fraction numerator C E over denominator C B end fraction.... left parenthesis i right parenthesis increment C F M tilde increment C D O space left square bracket A A right square bracket fraction numerator C F over denominator C D end fraction equals fraction numerator F M over denominator D O end fraction..... left parenthesis i i right parenthesis increment C E M tilde increment C B O fraction numerator C E over denominator C B end fraction equals fraction numerator M E over denominator B O end fraction fraction numerator F M over denominator D O end fraction equals fraction numerator M E over denominator B O end fraction A l s o comma space D O equals B O space left square bracket P r o v e d space E a r l i e r right square bracket therefore F E equals M E I n space increment A F M space a n d space increment A E M comma A M equals A M left square bracket C o m m o n space s i d e right square bracket angle A M F equals angle A M E equals 90 degree F E equals M E increment A F M space approximately equal to space increment A E M space left square bracket S A S right square bracket A r. increment A E M equals A r. increment A M F$

Answered by Prasenjit Paul | 3rd Mar, 2015, 11:30: AM

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