Question

on the sides AB and AC of triangle ABC,
equilateral triangles ABD and ACE are drawn.
Prove that: (i) angleCAD =angleBAE (ii) CD = BE.​

Answer 1

Answer:

Given:△ABD and △ACE are equilateral triangle.

∴ In △ABD

∠BAD=∠ABD=∠BDA=60

∘

.....(1)

In △ACE

∠AEC=∠ACE=∠ACE=60

∘

.....(2)

To prove:∠CAD=∠BAE

Proof:∠CAD=∠BAC+∠DAB

⇒∠CAD=∠BAC+60

∘

using (1)

⇒∠CAD=∠BAC+∠CAE using (2)

⇒∠CAD=∠BAE