D is any point on side AC of a ΔABC with AB = AC. Show that CD

Question

D is any point on side AC of a ΔABC with AB = AC. Show that CD < BD.

Philoid · Accepted Answer

Given: in ΔABC, AB = AC

In ΔABC,

AC = AB

∠ABC = ∠ACB (opposite angles to equal sides are equal)

In ΔABC and ΔDBC,

∠ABC > ∠DBC (since ∠DBC is interior angle of ∠ABC)

⇒ ∠ACB > ∠DBC (∵ ∠ABC = ∠ACB)

⇒ BD > CD (opposite sides to greater angle is greater)

Or CD < BD