In $\Delta ABC$,$\angle B = 50^{\circ}$ and $\angle C = 85^{\circ}$,then $AB$ $\dots$ $AC$.

$AD$ is a median of the triangle $ABC$. Is it true that $AB + BC + CA > 2AD$? Give reason for your answer.

In triangles $ABC$ and $PQR$,$\angle A = \angle Q$ and $\angle B = \angle R$. Which side of $\triangle PQR$ should be equal to side $AB$ of $\triangle ABC$ so that the two triangles are congruent? Give reason for your answer.

In triangles $ABC$ and $DEF$,$\angle A = \angle D$,$\angle B = \angle E$ and $AB = EF$. Will the two triangles be congruent? Give reasons for your answer.

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

$ABC$ is an isosceles triangle in which $AC = BC$. $AD$ and $BE$ are respectively two altitudes to sides $BC$ and $AC$. Prove that $AE = BD$.