# abc ia an isosceles triangle with ab=ac.and d is a point on ac such that bc square=ac*cd.prove tht bd=dc

In triangles BCD and ACB,

BC/CD=AC/BC

Now, Angle BCD=angle ACB (Common Angle)

Hence, the two triangles are similar by SAS rule.

So, angle DBC= angle DCB (as they are corresponding angles of similar triangles)

i.e. angle DBC=angle ACB (as ACB and DCB are one and the same angle)

At last, for triangle DBC,

DB=BC (as sides opp equal angles are equal).