The angle between the altitudes of a parallelogram, through the same vertex of an obtuse angle of the parallelogram is $60°$. Find the angles of the parallelogram.

In Figure, $ABCD$ and $AEFG$are parallelograms. If $\angle C={55}^{\mathrm{o}}$, what is the measure of $\angle F$?

In Figure, $BDEF$ and $DCEF$ are each a parallelogram. Is it true that $\mathrm{BD}=\mathrm{DC}$?

Why or why not?

In Figure, $\mathrm{BDEF} \mathrm{and} \mathrm{CEFD}$ are each a parallelogram.

Suppose it is known that $DE=DF$. Then, is $∆ABC$ Isosceles? Why or why not?

Diagonals of parallelogram $ABCD$ intersect at $O$ as shown in Figure. $XY$contains $O$, and $X,Y$ are points on opposite sides of the parallelogram. Give reason for the following:

$\mathrm{O}\mathrm{B}=\mathrm{O}\mathrm{D}$

Diagonals of parallelogram $ABCD$ intersect at $O$ as shown in Figure. $XY$contains $O$, and $X,Y$ are points on opposite sides of the parallelogram. Give reasons for the following:

$\angle OBY=\angle ODX$.

Diagonals of parallelogram $ABCD$ intersect at $O$ as shown in given figure. $XY$contains $O$ and $X,Y$ are points on opposite sides of the parallelogram. Give reasons for the following:

$\angle BOY=\angle DOX$

Diagonals of parallelogram $ABCD$ intersect at $O$ as shown in Fig. $XY$contains $O$, and $X,$$Y$are points on opposite sides of the parallelogram. Give reasons for the following:

$∆BOY\cong ∆DOX$.

Now, state if $XY$ is bisected at $O$.