If $\Delta XYZ$ has $XY = 7 \, cm$ and $YZ = 10 \, cm$,the perimeter of $\Delta XYZ$ is greater than how many centimeters?

$M$ is a point on side $BC$ of a triangle $ABC$ such that $AM$ is the bisector of $\angle BAC$. Is it true to say that the perimeter of the triangle is greater than $2\, AM$? Give reason for your answer.

$CDE$ is an equilateral triangle formed on side $CD$ of a square $ABCD$ (see figure). Show that $\triangle ADE \cong \triangle BCE$.

In the two triangles $ABC$ and $DEF$,$AB = DE$ and $AC = EF$. Name two angles from the two triangles that must be equal so that the two triangles are congruent. Give reason for your answer.

Two lines $l$ and $m$ intersect at the point $O$ and $P$ is a point on a line $n$ passing through the point $O$ such that $P$ is equidistant from $l$ and $m$. Prove that $n$ is the bisector of the angle formed by $l$ and $m$.

In the given figure,$PQ = PR$ and $\angle Q = \angle R$. Prove that $\triangle PQS \cong \triangle PRT$.