Question

in the given figure, D is the mid point of AB, DE || BC and DF || AC . Prove that: DE = BF. ​

Answer 1

In 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