Question

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

Answer 1

Given: An equilateral triangle CDE is on side CD of square ABCD

To prove: ΔADE ≅ ΔBCE

Proof: ∠EDC = ∠DCE = ∠CED = 60°(Angles of equilateral triangle)

∠ABC = ∠BCD = ∠CDA = ∠DAB = 90°(Angles of square)

∠EDA = ∠EDC + ∠CDA

= 60° + 90°

= 150°(i)

Similarly,

∠ECB = 150°(ii)

In ΔADE ≅ ΔBCE

ED = EC (Sides of equilateral triangle)

AD = BC (Sides of square)

∠EDA = ∠ECB [From (i) and (ii)]

Therefore, By SAS theorem

ΔADE ≅ ΔBCE