**Answer:**

In the image attached you can find the Unit 7 homework.

We need to findt he missing measures of each figure.

<h3>1.</h3>

Notice that the first figure is a rectangle, which means opposite sides are congruent so,

VY = 19

WX = 19

YX = 31

VW = 31

To find the diagonals we need to use Pythagorean's Theorem, where the diagonals are hypothenuses.

Also, , beacuse rectangles have congruent diagonals, which intercect equally.

That means,

<h3>2.</h3>

Figure number two is also a rectangle.

If GH = 14, that means diagonal GE = 28, because diagonals intersect in equal parts.

Now, GF = 11, because rectangles have opposite sides congruent.

DF = 28, because in a reactangle, diagonals are congruent.

HF = 14, because its half of a diagonal.

To find side DG, we need to use Pythagorean's Theorem, where GE is hypothenuse

<h3>3.</h3>

This figure is also a rectangle, which means all four interior angles are right, that is, equal to 90°, which means angle 11 and the 59° angle are complementary, so

Now, angles 11 and 4 are alternate interior angles which are congruent, because a rectangle has opposite congruent and parallel sides.

Which means , beacuse it's the complement for angle 4.

Now, , because it's a base angle of a isosceles triangle. Remember that in a rectangle, diagonals are congruent, and they intersect equally, which creates isosceles triangles.

, by interior angles theorem.

, by vertical angles theorem.

, by supplementary angles.

, by vertical angles theorem.

, by complementary angles.

, by alternate interior angles.

, by complementary angles.

<h3>4.</h3>

, because it's one of the four interior angles of a rectangle, which by deifnition are equal to 90°.

, by alternate interior angles and by given., by complementary angles.

, by complementary angles.

, by interior angles theorem.

, by supplementary angles.

<h3>5.</h3>

, by supplementary angles.

, by interior angles theorem, and by isosceles triangle theorem.

, by definition of rectangle.

, by interior angles theorem, and by isosceles triangle theorem.

, by complementary angles.

, by alternate interior angles.

<h3>6.</h3>

The figure is a rectangle, which means its opposite sides are equal, so

Then, we replace this value in the expression of side WZ

Therefore, side WZ is 29 units long.

<h3>7.</h3>

We know that the diagonals of a rectangle are congruent, so

Then,

Therefore, side PR is 73 units long.