Question

CDE is an equilateral triangle formed on a side CD of a square ABCD (Figure). Show that ∆ADE ≅ ∆BCE.

Answer 1

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

To proof that ΔADE ≅ ∆BCE

Proof: In triangle ADE and triangle BCE,

DE = CE  ...[Side of an equilateral triangle]

∠ADE = ∠BCE

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

∠ADE = 90° + 60° = 150° and ∠BCE = 90° + 60° = 150°

AD = BC  ...[Sides of a square]

∆ADE ≅ ∆BCE   ...[By SAS congruence rule]