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:
AB = CE

Answer 1

In ΔABD and ΔDCE
BD = CD  ...(D is mid-point of BC)
∠ADB = ∠DCE   ...(proved)
AD = CE  ...(since AD = AC and AC = CE)
Therefore, ΔABD ≅ ΔDCE
Hence, AB = CE.