The ratio of the corresponding sides of two similar triangles is $4:9$. Then,the ratio of their areas is $\ldots \ldots$.

Which of the following correctly matches the information in Part $I$ and Part $II$?

Part $I$	Part $II$
$1.$ In $\Delta ABC$ and $\Delta PQR, \angle A \cong \angle P$ and $\angle C \cong \angle Q$	$a.$ Correspondence $ABC \leftrightarrow RQP$ is a similarity.
$2.$ In $\Delta ABC$ and $\Delta PQR, \frac{AB}{QR} = \frac{BC}{PQ}$ and $\angle B \cong \angle Q$	$b.$ Correspondence $ABC \leftrightarrow QPR$ is a similarity.
$3.$ In $\Delta ABC$ and $\Delta PQR, \frac{AB}{PQ} = \frac{BC}{PR} = \frac{CA}{QR}$	$c.$ Correspondence $ABC \leftrightarrow PQR$ is a similarity.
$4.$ In $\Delta ABC$ and $\Delta PQR, \frac{AB}{PQ} = \frac{CA}{PR}$ and $\angle A \cong \angle P$	$d.$ Correspondence $ABC \leftrightarrow PRQ$ is a similarity.

In $\Delta ABC$,$P$,$Q$,and $R$ are the midpoints of $\overline{AB}$,$\overline{BC}$,and $\overline{CA}$ respectively. Then,which of the following statements is not true?

In $\Delta PQR$,$P-X-Q$,$P-Y-R$ and $\overline{XY} \parallel \overline{QR}$. If $PX = 3$,$PQ = 8$ and $PY = 4.2$,find $YR$.

In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude. If $AC = 13$ and $CM = 9$,then $BM = \ldots \ldots$

In rhombus $ABCD$,$AC > BD$ and $\overline{AC} \cap \overline{BD} = \{M\}$. If $AM + DM = 17$ and $AB = 13$,find $BD$.