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

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

To prove:

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

ABC = BCD = CDA = DAB = 90o (Angles of square)

EDA = EDC + CDA

= 60o + 90o

= 150o (i)

Similarly,

ECB = 150o (ii)

In

ED = EC (Sides of equilateral triangle)

AD = BC (Sides of square)

EDA = ECB [From (i) and (ii)]

Therefore, By SAS theorem

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