Question

In ΔABC, D is the mid-point of BC, AD is equal to AC. AC is produced to E, such that CE = AC. Prove that:
∠ADB = ∠DCE

Answer 1

In ΔADC,
AD = AC  ...(given)
Therefore, ∠ADC = ∠ACD ..........(i)
But ∠ADB + ∠ADC = 180°  ........(ii)
And ∠ACD + ∠DCE = 180° ........(iii)
From (i), (ii) and (iii)
∠ADB = ∠DCE.