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

Question

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

Philoid · Accepted Answer

Given: CDE is an equilateral triangle formed on a side CD of a square ABCD.

In ΔADE and ΔBCE,

DE = CE (sides of equilateral triangle)

Now, ∠ADC = ∠BCD = 90° and ∠EDC = ∠ECD = 60°

Hence, ∠ADE = ∠ADC + ∠CDE = 90° + 60° = 150°

And ∠BCE = ∠BCD + ∠ECD = 90° + 60° = 150°

⇒ ∠ADE = ∠BCE

AD = BC (sides of square)

Hence, ΔADE ≅ΔBCE (by SAS)