Use the diagonals to tell whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Give all the names that apply. $Q(-8,-2), T(-6,8), W(4,6), Z(2,-4)$

Show that the diagonals of the square with the given vertices are congruent perpendicular bisectors of each other. $R(-5,0), S(-1,-2), T(-3,-6)$, and $U(-7,-4)$

Tell whether the polygon is regular or irregular. Then tell whether it is concave or convex.

Tell whether each statement is sometimes, always, or never true. A pair of consecutive angles in a kite are supplementary.

Tell whether each statement is sometimes, always, or never true. The opposite angles of a trapezold are supplementary.

Each square section in an iron railing contains four small kites. The figure shows the dimensions of one kite. What length of iron is needed to outline one small kite? How much iron is needed to outline one complete section, including the square? Explain how each answer was found.

The edges of the kite-shaped glass in the sun catcher are sealed with lead strips. JH, KH, and LH are 2.75 inches, and MH is 5.5 inches. How much lead is needed to seal the edges of the sun catcher? If the craftsperson has two 3-foot lengths of lead, how many sun catchers can be sealed ?

In trapezoid PRSV, name the bases, the legs, and the mid segment.

Write a two-column proof of Theorem 6-5-1.

Given: ABCD is a parallelogram. $\angle A$ is a right angle.

Prove: ABCD is a rectangle.

The diagonals of a quadrilateral are perpendicular bisectors of each other. What is the best name for this quadrilateral? Explain your answer.

Find the value of $x$ that makes the parallelogram the given type.

Rectangle

Find the value of x that makes the parallelogram the given type.

rhombus

The coordinates of three vertices of a parallelogram ABCD are given. Find the coordinates of D so that the given type of figure is formed.

$A(2,1), B(-1,5), C(-5,2)$; square

The coordinates of three vertices of a parallelogram ABCD are given. Find the coordinates of D so that the given type of figure is formed.

$A(-5,5), B(0,0), C(7,1)$; rhombus