Question

Prove that the four triangles formed by joining in pairs, the mid-points of three sides of a triangle, are congruent to each other.

Easy

Solution

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Given :

A triangle of and are  the mid-points of sides and respectively.

To prove :

.

Proof :

Since the segment joining the mid-points of the sides of a triangle is half of the third side. Therefore,

          ..........(1)

           .........(2)

           ..........(3)

Now, in and  



and,

So, by SSS criterion of congruence,


Similarly, and

Hence,

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