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,
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
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.
, 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.
, 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.
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.
