Prove that the straight line joining the vertex of an isosceles triangle to any point in the base is smaller than either of the equal sides of the triangle.

In the following diagram; AD = AB and AE bisects angle A. Prove that :

(i) BE = DE

(ii) ∠ABD > ∠C

In the given figure, AD = AC and B is a point on CD produced, show that AB > AD.

S is any point on side QR of triangle PQR. Prove that :

PQ + QR + RP > 2PS