Question

draw the answer of this question
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Answer 1

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ANSWER

In ΔABC, D,E and F are the mid points of sides AB,BC and AC respectively.

Since in ΔABC, F is the midpoint of AC and D is the mid point of AB, therefore,

FD=

2

1

CB and FD∥CB ( by mid point theorem)

⇒FD=CE and FD∥CE ..........(1)

Similarly,

DE=FC and DE∥FC .........(2)

FE=DB and FE∥DB .........(3)

Therefore from the equations (1), (2) and (3), we get,

ADEF,DBEF and DECF are parallelograms.

The diagonal of a parallelogram divide it into two triangles which will be congruent to each other, thus,

ΔDEF≅ΔADF ............(4)

ΔDEF≅ΔDBE .........(5)

ΔDEF≅ΔFEC ..........(6)

From equations (4), (5) and (6), we get

ΔDEF≅ΔECF≅ΔDBE≅ΔADF