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

In $\Delta ABC$,$AB = AC$ and $\angle CAD$ is an exterior angle of $\Delta ABC$ at vertex $A$. If ray $AP$ is the bisector of $\angle CAD$,then prove that $AP \parallel BC$.

$D$ is any point on side $AC$ of a $\triangle ABC$ with $AB = AC$. Show that $CD < BD$.

Is it possible to construct a triangle with lengths of its sides as $8\,cm, 7\,cm$ and $4\,cm$? Give reason for your answer.

If $\Delta PRQ \cong \Delta ZXY,$ then in $\Delta XYZ,$ which angle is equal to $\angle R$?

In the given figure,$l \parallel m$ and $M$ is the mid-point of a line segment $AB$. Show that $M$ is also the mid-point of any line segment $CD,$ having its end points on $l$ and $m,$ respectively.