Question

D,E and F are the mid point of the side AB,BC and CA of an isosceles triangle ABC in which AB =BC . Prove that triangle DEF is also isosceles
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Answer 1

Answer:

Given: △ABC, AB=BC, D, E and F are mid points of AB, BC and CA respectively.

Since, D is mid point of AB and E is mid point of BC

By Mid point theorem, DF∥AC and DF=

2

1

AC...(1)

Since, E is mid point of BC and F is mid point of AC

By Mid point theorem, EF∥AB and EF=

2

1

AB ...(2)

Hence, By (1) and (2)

DE=EF

or △DEF is an isosceles triangle.

Answer 2

QUESTION:

• D,E and F are the mid point of the side AB,BC and CA of an isosceles triangle ABC in which AB =BC . Prove that triangle DEF is also isosceles
• D,E and F are the mid point of the side AB,BC and CA of an isosceles triangle ABC in which AB =BC . Prove that triangle DEF is also isosceles

SOLUTION:

• Given that ABC is an isosceles triangle where AB = AC

Since D, E, F are the mid-point of AB, BC, CA therefore

• 2DE = AC

and

• 2EF = AB (this means DE = EF)

Therefore DEF is an isosceles triangle a DE = EF.

Therefore DEF is an isosceles triangle a DE = EF.Hence proved