In $\triangle PQR$,$\angle R = \angle P$,$QR = 4 \, cm$,and $PR = 5 \, cm$. Then the length of $PQ$ is (in $cm$):

In the given figure,$PN$ and $QM$ are both perpendicular to line segment $PQ$. Also,$X$ is the midpoint of $PQ$ as well as $MN$. Prove that $\triangle PNX \cong \triangle QMX$.

Measure of each exterior angle of an equilateral triangle is $\ldots \ldots \ldots$ (in $^{\circ}$)

For any convex quadrilateral $ABCD$,prove that $AB + BC + CD + DA < 2(AC + BD)$.

$D$ is a point on the side $BC$ of a $\triangle ABC$ such that $AD$ bisects $\angle BAC$. Then

Prove that in a triangle,other than an equilateral triangle,the angle opposite to the longest side is greater than $\frac{2}{3}$ of a right angle.