Question

In the adjoining figure, ABCD is a square and
∆EDC is an equilateral triangle. Prove that
(i) AE = BE, (ii) DAE = 15°.​

Answer 1

Answer:

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Step-by-step explanation:

Given: ABCD is a square and EDC is an equilateral triangle.

To prove: AE=BE and  

Proof: In  

          AD=BD             ( Side of same square)

     ∠ADE=∠BCE         (Each angle is 150°)

          DE=BE             ( Side of same equilateral triangle)

So,  by SAS congruence

Therefore,  AE=BE   (By CPCT )

Hence Proved

In  

AD=DE

 (If sides of a triangle are equal then their opposites angles are equal)

In  

Angle sum property of triangle

 

Hence Proved