Question

Prove that the triangle obtained by joining the mid-points of the sides of an isosceles triangles is also an isosceles triangle.

Answer 1

Answer:

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Answer 2

Let ABC be an isosceles triangle where AB=AC

Now, D,E,F are mid points and they are joined to form a triangle DEF

Now, What we have to do is that we have to prove that Triangle DEF is also an isosceles triangle

So.

To Prove:Triangle DEF is an isosceles triangle

Proof

IN triangle ABC,By Mid-point theoram,

ED=1/2BC .....(i)

EF=1/2AC .....(ii)

FD=1/2AB .....(iii)

And,

Since, D and F are mid points

AB=AC

And there half must be also equal

So ,

1/AC=1/AB

Therefore on comparing (ii) and (iii)

EF=FD

Since In triangle DEF,

Two opposite sides EF and DF are equal

Therefore the triangle so formed by joining the mid-point of Triangle ABC is also an isosceles triangle.

Hence, Triangle DEF is an isosceles triangle

Hence,it is proved