In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM = 5$,$MB = 8$ and $AN = 10$,then $NC = \dots$

In $\Delta PQR$,$m\angle Q = 90^\circ$. If $PQ = 8$ and $QR = 15$,then $PR = \ldots$

If $\triangle ABC \sim \triangle EDF$ and $\triangle ABC$ is not similar to $\triangle DEF$,then which of the following is not true?

In $\Delta ABC$,$\overline{AD}$ is a median. If $AB = 8$,$AC = 15$ and $AD = 8.5$,find $BC$.

Transversals $t_{1}$ and $t_{2}$ to $l_{1} \parallel l_{2} \parallel l_{3}$ intersect them at $A, B, C$ and $P, Q, R$ respectively. If $AB = 5$,$BC = 8$ and $PQ = 6.5$,find $QR$.

The length of a diagonal of a square is $6$. Then,its area is............