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

In a right triangle,prove that the line segment joining the mid-point of the hypotenuse to the opposite vertex is half the length of the hypotenuse.

Line segments $AB$ and $CD$ bisect each other at $P$. If $PA = PD$ and $PB = PC$,prove that $AC = BD$.

In $\Delta ABC$,$\angle A = 90^{\circ}$ and $AB = AC$. The bisector of $\angle A$ meets $BC$ at $D$. Prove that $BC = 2 AD$.

Two sides of a triangle are of lengths $5\, cm$ and $1.5\, cm$. The length of the third side of the triangle cannot be (in $cm$):

Prove that an angle opposite to the longest side in a scalene triangle is greater than $60^{\circ}$.