Question

on the side AB and AC of triange ABC, equilateral triangle ABD and ACE are drawn .
prove that: angle CAD = angle CD=BE

Answer 1

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Answer 2

Answer:

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.