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Question

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

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Solution


Given : ABCD is a square and EDC is an equilateral triangle. AD=BC=CD=DE=CE
To Prove : i) AE=BE
ii) DAE=15
Construction : Join A to E and B to E.
Proof :
i) In ADE and BCE, we have
AD=BC(given)
ADE=BCE(=90+60)
DE=CE(given)
Therefore, ADEBCE (By SAS rule)
AE=BE (CPCT)

ii) DAE+ADE+DEA=180 [Angle sum property]
150+DAE+DEA=180
DAE+DEA=180150 [AD=ED, angle opposite to equal sides are equal, DAE=DEA ]
2DAE=30
DAE=15


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