Question

ABC is a triangle and D is the midpoint of BC. The perpendiculars from D to

AB and AC are equal. Prove that the triangle is isosceles.​

Answer 1

Answer:

ANSWER

Let DE and DF be the perpendiculars from D on AB and AC respectively.

In △s BDE and CDF, DE=DF (Given)

∠BED=∠CFD=90

∘

BD=DC (∵ D is the mid-point of BC)

∴ △BDE≅△CDF (RHS)

⇒ ∠B=∠C (cpct)

⇒ AC=AB (Sides opp. equal ∠s are equal)

⇒ △ABC is isosceles.