Question

ABC is a triangle and D is the mid-point of BC. The Perpendicular from
D to AB and AC are equal. Prove that triangle is isosceles.​

Answer 1

Answer: ABC

Step-by-step explanation: 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.