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Question

In a ABC, D is the midpoint of the side BC.DE is perpendicular to AB and DF is perpendicular to AC. Also, DE=DF, Then B =
  1. C
  2. F
  3. A
  4. E

A
E
B
C
C
F
D
A
Solution
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Given: D is the midpoint of BC

BD=DC

Also, DE=DF

DE is perpendicular to AB

E=90o

DF is perpendicular to AC

F=90o

If we consider two triangles so formed, ΔDEB and ΔCFD, then their hypotenuse BD and CD are equal.

E=F=90o. Also DE=CF.

Thus according to R.H.S condition of congruence ΔDEBΔCFD

Thus, the corresponding angles B and C are equal, i.e B=C

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