Q. 85.0( 5 Votes )

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

Answer :


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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