Question

Angle ABC is an equilateral triangle. If AB//CE, prove that angle ACE = angle ECD.

Answer 1

The proof is as follows:

Given:

Triangle ABD and Triangle ACE are equilateral triangles.

To Prove:−

∠ CAD = ∠ BAE

CD =BE

Proof:−

∠ CAD = ∠ CAB + ∠BAD

∠ CAD =∠ CAB + 60° (Since ∠ BAD=60°)

∠CAD = ∠ CAB + ∠ CAE (Since ∠ CAE=60°)

∠ CAD =∠BAE

Hence Proved.

In Triangle CAD and Triangle BAE

BA = AD

Angle CAD = Angle BAE (Proved above)

AC = AE

Triangle CAD ≅ Triangle BAE

So, CD = BE

Hence Proved.