91Ó°ÊÓ

Given:$\mathbf{ABCD}$is a parallelogram;$\stackrel{¯}{\mathrm{AD}}â‰\dots \stackrel{¯}{\mathrm{AC}}$;$\stackrel{¯}{\mathrm{AE}}â‰\dots \stackrel{¯}{\mathrm{EC}}$;$∠\mathbf{ADF}â‰\dots ∠\mathbf{CDF}$;$\mathbf{m}∠\mathbf{DAC}\mathbf{=}\mathbf{36}$.

Complete each statement about the diagram.

$\mathbf{m}∠\mathbf{DAC}\mathbf{=}\mathbf{36}$, so $\mathbf{m}∠\mathrm{ADC}=\underset{\_}{?}$ and $\mathbf{m}∠\mathrm{ADF}=\underset{\_}{?}$.

$\stackrel{¯}{\mathrm{MN}}$is the median of trapezoid $\mathbf{ZOID}$.

If$\mathbf{ZO}\mathbf{=}\mathbf{8}$ , then$\mathrm{TN}=\underset{\_}{?}$ .

Each figure in Exercises 19-24 is a parallelogram with its diagonals drawn. Find the values of x and y.

What values must x and y have to make the quadrilateral a parallelogram?

$\stackrel{¯}{\mathit{M}\mathit{N}}$is the median of trapezoid $ZOID$.

If trapezoid ZOID is isosceles and localid="1638356865991" $\mathrm{m}∠\mathrm{D}=80$, then localid="1638356856943" $\mathrm{m}∠\mathrm{O}=\underset{¯}{?}$.

A skew quadrilateral SKEW is shown. M, N, O, and P are the midpoints of $\stackrel{¯}{SK},\stackrel{¯}{KE},\stackrel{¯}{WE}$and $\stackrel{¯}{SW}$ . Explain why PMNO is a parallelogram.

The coordinates of the three vertices of a rectangle are given. Plot the points and find the coordinates of the fourth vertex. State whether the rectangle is a square.

$\text{O}\left(0,0\right)\text{,E}\left(4,0\right)\text{,F}\left(4,3\right)\text{,G}\left(\underset{¯}{?},\underset{¯}{?}\right)$.

Draw a quadrilateral of the type named. Join, in order, the midpoints of the sides. What special kind of quadrilateral do you appear to get?

Rectangle

Given:$\mathbf{ABCD}$is a parallelogram;$\stackrel{¯}{\mathrm{AD}}â‰\dots \stackrel{¯}{\mathrm{AC}}$;$\stackrel{¯}{\mathrm{AE}}â‰\dots \stackrel{¯}{\mathrm{EC}}$;$∠\mathbf{ADF}â‰\dots ∠\mathbf{CDF}$;$\mathbf{m}∠\mathbf{DAC}\mathbf{=}\mathbf{36}$.

Complete each statement about the diagram.

$â–³\mathbf{ADF}$is a(n)$\underset{\_}{?}$ triangle.

$\stackrel{¯}{\mathrm{MN}}$is the median of trapezoid$\mathbf{ZOID}$ .

If trapezoid$\mathbf{ZOID}$ is isosceles and$\mathbf{m}∠\mathbf{D}\mathbf{=}\mathbf{80}$ , then $\mathbf{m}∠O=\underset{\_}{?}$.