Question

ABC is a triangle and D is the mid-point of BC the perpendiculars from D to AB and AC are equal prove that the triangle is isosceles

Answer 1

Given :

• ABC is a triangle
• D is the mid point of BC
• the perpendiculars from D to AB and AC are equal. [ ED = DF ]

To be prove :

• the triangle is isosceles

Proof :

In △BED and △DFC

∠BED = ∠DFC = 90°

ED = DF | Given

BD = DC | D is the mid point of

BC

Hence,△ BED ≅ △DFC. | by R.H.S

congruence criteria.

Therefore, ∠ B = ∠ C | by C.P.C.T

Hence, the △ABC is a isosceles triangle.

____________________

Hope it helps you.

Please mark me as brainliest.