Question

2. In the given figure, ABC is a triangle with D as the
mid point of AB, DE 1 AC, DF 1 BC. Also DE = DF. .
Prove that AABC is an isosceles triangle.​

Answer 1

triangle ABC

D is the midpoint of BC

DE perpendicular to AB

And DF perpendicular to AC

DE=DF

To prove:

Triangle ABC is an isosceles triangle

Proof:

In the right angles triangle BED and CDF

Hypotenuse BD=DC ( because D is a midpoint )

Side DF=DE ( given)

△BED≅CDF ( RHS axiom)

∠C=∠B

AB=AC ( sides opposite to equal angles

△ABC is an isosceles triangle