Diagonals of a rectangle are equal and perpendicular. Is this statement true? Give reason for your answer.

Diagonals $AC$ and $BD$ of a quadrilateral intersect each other at $O$ such that $OA:OC=3:2$. Is $ABCD$ a parallelogram? Why or why not?

In the given rhombus $\mathrm{ABCD}, \angle \mathrm{BAC}=35°$. If $\angle \mathrm{ABO}=k°$, find $k$.

In the adjoining rhombus $\mathrm{ABCD}, \angle \mathrm{BAC}=35°$. If $\angle \mathrm{BCD}=k°$, find $k$.
 

In the adjoining rhombus $\mathrm{ABCD}, \angle \mathrm{BAC}=35°$. If $\angle \mathrm{CDA}=k°$, find $k$.