In $\Delta ABC$,$m \angle A = 90^\circ$. If $b = 12$ and $c = 35$,then $a = \ldots$

In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{O\}$. If $\frac{OA}{OC} = \frac{1}{2}$ and $AB = 5$,find $CD$.

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

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{AD}$ is a median. Prove that $AC^{2} = AD^{2} + 3BD^{2}$.

$ABCD$ is a rectangle. If $AB = 7.5$ and $AC = 19.5$,find $BC$.

In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QD}$ is an altitude. If $PD = 9 DR$,then $PQ = \ldots \ldots \ldots \times QR$.