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