Question

in the adjoining figure ABCD is a square and CE = AF prove that DCE = CTA

Answer 1

 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.