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 = 60^{o} (Angles of equilateral triangle)

∠ABC = ∠BCD = ∠CDA = ∠DAB = 90^{o} (Angles of square)

∠EDA = ∠EDC + ∠CDA

= 60^{o} + 90^{o}

= 150^{o} (i)

Similarly,

∠ECB = 150^{o} (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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