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In the adjoining figure, ABCD is …

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In the adjoining figure, ABCD is a square and triangle EDC is an equilateral triangle. Prove that angle DAE=15 degree

Posted by Vanshikha Upadhyay 8 years, 6 months ago

CBSE > Class 09 > Mathematics

2 answers

Harshavardhan Shinde 8 years, 6 months ago

Construction : Join A to E and B to E.
Proof :
i) In ΔADE and ΔBCE,
AD = BC (given)
∠ADE = ∠BCE (90° + 60°)
DE = CE (given)
Therefore, ΔADE is congruent to ΔBCE ( SAS rule)
AE = BE (CPCTC)

ii) ∠DAE + ∠ADE + ∠DEA = 180°
150° + ∠DAE + ∠DEA = 180°
∠DAE + ∠DEA = 180° -150°
2 ∠DAE = 30°
∠DAE = 15°
Hence Proved.

1Thank You

Harshavardhan Shinde 8 years, 6 months ago

∠DAE + ∠ADE + ∠DEA = 180°
150° + ∠DAE + ∠DEA = 180°
∠DAE + ∠DEA = 180° -150°
2 ∠DAE = 30°
∠DAE = 15°
Hence Proved.

0Thank You

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CBSE > Class 09 > Mathematics