If in $\Delta ABC, AC > AB > BC$,then find the greatest angle of the triangle.

Bisectors of the angles $B$ and $C$ of an isosceles triangle $ABC$ with $AB = AC$ intersect each other at $O$. Show that the external angle adjacent to $\angle ABC$ is equal to $\angle BOC$.

In $\Delta ABC$,$AB = AC$ and $AD$ is an altitude to the base $BC$. Prove that $D$ is the midpoint of $BC$.

There can be $\ldots \ldots \ldots$ one-one correspondences between two triangles.

In quadrilateral $PQRS$,$PQ = PS$ and $RQ = RS$. Prove that $\angle PQR = \angle PSR$.

The image of an object placed at a point $A$ before a plane mirror $LM$ is seen at the point $B$ by an observer at $D$ as shown in the figure. Prove that the image is as far behind the mirror as the object is in front of the mirror.