Given: △ABC, BC>AC, D∈ AC, CD=CB Prove: m∠ABD is acute

Step-by-step explanation:

Given: △ABC, BC>AC, D∈ AC, CD=CB

To prove: m∠ABD is acute

Proof: In ΔABC, the angle opposite to side BC is ∠BAC and the angle opposite to side AC is ∠ABC.

Now, it is given that BC>AC, then ∠BAC>∠ABC ... (1)

In ΔBDC, using the exterior angle property,

∠ADB=∠DBC+∠BCD

∠ADB=∠DBC+∠BCA

⇒∠ADB>∠BAC (2)

From equation (1) and (2), we get

∠ADB>∠BAC

⇒∠ADB>∠ABC

⇒DB>AB

Hence, m∠ABD is acute