Question

in figure, ABCD is a square and ∆ DCE is equilateral. prove that

1) AE = BE
2) Angle EBC = 15°​

Answer 1

Answer:

Given : ABCD is a square and EDC is an equilateral triangle. AD = BC, DE = CE

To Prove : i) AE = BE

              ii) ∠DAE = 15°

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.

Step-by-step explanation: