If $\Delta ABC \cong \Delta YZX,$ then in $\Delta XYZ,$ which side is equal to side $AB$?

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 $\angle BOC$.

$S$ is any point on side $QR$ of a $\triangle PQR$. Show that: $PQ + QR + RP > 2 \, PS$.

For any convex quadrilateral $ABCD$,prove that $AB + BC + CD + DA > AC + BD$.

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

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