Question

CDE is an equilateral triangle formed on a side CD of a square ABCD. Show that ΔADE ≅ΔBCE.

Answer 1

We have to prove that  ΔADE ≅ ΔBCE

Given  ABCDis a square

So  AB = BC = CD = AD

Now in ΔEDC is equilateral triangle.

So  DE = EC = CB

In ΔAED and  ΔCEB

 AD = BC (Side of triangle)

DE = CE (Side of equilateral triangle)

∠ADE = ∠ADC + ∠CDE

= 90 + 60 

= 150

And,

∠BCE = ∠BCD + ∠DCE

         = 90 + 60 

          = 150

So ∠ACE = ∠BCDE

Hence from SAS congruence  ΔADE ≅ ΔBCE Proved.