Title: Chapter 8
Course: quiz duplicate error

Q: Find the measure of each interior angle for a regular pentagon. Round to the nearest tenth if necessary.
- 360 (To find the size of each interior angle of a regular polygon, use the formula [Image].)
- 108 (To find the size of each interior angle of a regular polygon, use the formula [Image].)
- 540 (To find the size of each interior angle of a regular polygon, use the formula [Image].)
- 72 (To find the size of each interior angle of a regular polygon, use the formula [Image].)
A: 108

Q: Find the measure of an interior angle of a regular polygon with 14 sides. Round to the nearest tenth if necessary.
- 2160 (To find the size of each interior angle of a regular polygon, use the formula [Image].)
- 25.7 (To find the size of each interior angle of a regular polygon, use the formula [Image].)
- 154.3 (To find the size of each interior angle of a regular polygon, use the formula [Image].)
- 360 (To find the size of each interior angle of a regular polygon, use the formula [Image].)
A: 154.3

Q: Find the measure of each exterior angle for a regular nonagon. Round to the nearest tenth if necessary.
- 1260 (To find the size of each exterior angle of a regular polygon, use the formula [Image].)
- 140 (To find the size of each exterior angle of a regular polygon, use the formula [Image].)
- 360 (To find the size of each exterior angle of a regular polygon, use the formula [Image].)
- 40 (To find the size of each exterior angle of a regular polygon, use the formula [Image].)
A: 40

Q: Find the measure of an exterior angle of a regular polygon with 20 sides. Round to the nearest tenth if necessary.
- 360 (To find the size of each exterior angle of a regular polygon, use the formula [Image].)
- 3240 (To find the size of each exterior angle of a regular polygon, use the formula [Image].)
- 162 (To find the size of each exterior angle of a regular polygon, use the formula [Image].)
- 18 (To find the size of each exterior angle of a regular polygon, use the formula [Image].)
A: 18

Q: Complete the statement about parallelogram ABCD.
[Image]

[Image]____
- [Image]; Alternate interior angles are congruent. (Locate the angle on the parallelogram. Using the properties of parallelograms, determine which angle is congruent to that angle.)
- [Image]; Alternate interior angles are congruent. (Locate the angle on the parallelogram. Using the properties of parallelograms, determine which angle is congruent to that angle.)
- [Image]; Opposite angles of parallelograms are congruent. (Locate the angle on the parallelogram. Using the properties of parallelograms, determine which angle is congruent to that angle.)
- [Image]; Opposite angles of parallelograms are congruent. (Locate the angle on the parallelogram. Using the properties of parallelograms, determine which angle is congruent to that angle.)
A: [Image]; Alternate interior angles are congruent. / [Image]; Opposite angles of parallelograms are congruent.

Q: Complete the statement about parallelogram ABCD.
[Image]

[Image]
- [Image]; Opposite sides of parallelograms are congruent. (Locate the indicated segment on the parallelogram. Using the properties of parallelograms, determine which segment is congruent to that segment.)
- [Image]; Diagonals of parallelograms bisect each other. (Locate the indicated segment on the parallelogram. Using the properties of parallelograms, determine which segment is congruent to that segment.)
- [Image]; Opposite sides of parallelograms are congruent. (Locate the indicated segment on the parallelogram. Using the properties of parallelograms, determine which segment is congruent to that segment.)
- [Image]; Diagonals of parallelograms bisect each other. (Locate the indicated segment on the parallelogram. Using the properties of parallelograms, determine which segment is congruent to that segment.)
A: [Image]; Opposite sides of parallelograms are congruent.

Q: Refer to parallelogram ABCD to answer to following questions.
[Image]

What is the length of segment AK?
- [Image] (Use the distance formula to determine the missing length. The distance formula is [Image].)
- [Image] (Use the distance formula to determine the missing length. The distance formula is [Image].)
- [Image] (Use the distance formula to determine the missing length. The distance formula is [Image].)
- [Image] (Use the distance formula to determine the missing length. The distance formula is [Image].)
A: [Image]

Q: Refer to parallelogram ABCD to answer to following questions.
[Image]

What is the distance between points A and C?
- [Image] (Use the distance formula to determine the missing length. The distance formula is [Image].)
- [Image] (Use the distance formula to determine the missing length. The distance formula is [Image].)
- [Image] (Use the distance formula to determine the missing length. The distance formula is [Image].)
- [Image] (Use the distance formula to determine the missing length. The distance formula is [Image].)
A: [Image]

Q: Refer to parallelogram ABCD to answer to following questions.
[Image]

What is the length of segment DK?
- [Image] (Use the distance formula to determine the missing length. The distance formula is [Image].)
- [Image] (Use the distance formula to determine the missing length. The distance formula is [Image].)
- [Image] (Use the distance formula to determine the missing length. The distance formula is [Image].)
- [Image] (Use the distance formula to determine the missing length. The distance formula is [Image].)
A: [Image]

Q: Refer to parallelogram ABCD to answer to following questions.
[Image]

Do the diagonals bisect each other? Justify your answer.
- yes; [Image] and [Image] (Use the distance formula to determine the lengths of the segments. The distance formula is [Image]. In order for the diagonals to be bisected, each segment of the diagonal should be congruent.)
- yes; The diagonals are not congruent. (Use the distance formula to determine the lengths of the segments. The distance formula is [Image]. In order for the diagonals to be bisected, each segment of the diagonal should be congruent.)
- no; [Image] and [Image] (Use the distance formula to determine the lengths of the segments. The distance formula is [Image]. In order for the diagonals to be bisected, each segment of the diagonal should be congruent.)
- no; The diagonals are not congruent. (Use the distance formula to determine the lengths of the segments. The distance formula is [Image]. In order for the diagonals to be bisected, each segment of the diagonal should be congruent.)
A: yes; [Image] and [Image]

Q: Refer to parallelogram ABCD to answer to following questions.
[Image]

Are the diagonals congruent? Justify your answer.
- yes; Both diagonals have a length of [Image]. (Use the distance formula to determine the lengths of the diagonals. The distance formula is [Image]. If the lengths are the same, then the diagonals are congruent.)
- yes; Both diagonals have a length of [Image]. (Use the distance formula to determine the lengths of the diagonals. The distance formula is [Image]. If the lengths are the same, then the diagonals are congruent.)
- yes; Both diagonals have a length of [Image]. (Use the distance formula to determine the lengths of the diagonals. The distance formula is [Image]. If the lengths are the same, then the diagonals are congruent.)
- no; The lengths of the diagonals are not the same. (Use the distance formula to determine the lengths of the diagonals. The distance formula is [Image]. If the lengths are the same, then the diagonals are congruent.)
A: no; The lengths of the diagonals are not the same.

Q: Refer to parallelogram ABCD to answer the following questions.
[Image]

Do the diagonals bisect each other? Justify your answer.
- yes; [Image] and [Image]. (Use the distance formula to determine the lengths of the segments. The distance formula is [Image]. In order for the diagonals to be bisected, each segment of the diagonal should be congruent.)
- yes; The diagonals are not congruent. (Use the distance formula to determine the lengths of the segments. The distance formula is [Image]. In order for the diagonals to be bisected, each segment of the diagonal should be congruent.)
- no; [Image] and [Image]. (Use the distance formula to determine the lengths of the segments. The distance formula is [Image]. In order for the diagonals to be bisected, each segment of the diagonal should be congruent.)
- no; The diagonals are not congruent. (Use the distance formula to determine the lengths of the segments. The distance formula is [Image]. In order for the diagonals to be bisected, each segment of the diagonal should be congruent.)
A: yes; [Image] and [Image].

Q: Refer to parallelogram ABCD to answer the following questions.
[Image]

Are the diagonals congruent? Justify your answer.
- yes; Both diagonals have a length of [Image]. (Use the distance formula to determine the lengths of the diagonals. The distance formula is [Image]. If the lengths are the same, then the diagonals are congruent.)
- yes; Both diagonals have a length of [Image]. (Use the distance formula to determine the lengths of the diagonals. The distance formula is [Image]. If the lengths are the same, then the diagonals are congruent.)
- yes; Both diagonals have a length of [Image]. (Use the distance formula to determine the lengths of the diagonals. The distance formula is [Image]. If the lengths are the same, then the diagonals are congruent.)
- no; The lengths of the diagonals are not the same. (Use the distance formula to determine the lengths of the diagonals. The distance formula is [Image]. If the lengths are the same, then the diagonals are congruent.)
A: no; The lengths of the diagonals are not the same.

Q: Refer to parallelogram ABCD to answer the following questions.
[Image]

What is the length of segment BD?
- [Image] (Use the distance formula to determine the length of BD. The distance formula is [Image].)
- [Image] (Use the distance formula to determine the length of BD. The distance formula is [Image].)
- [Image] (Use the distance formula to determine the length of BD. The distance formula is [Image].)
- [Image] (Use the distance formula to determine the length of BD. The distance formula is [Image].)
A: [Image]

Q: Determine whether the quadrilateral is a parallelogram. Justify your answer.

[Image]
- no; Opposite angles are congruent. (Using the properties of parallelograms, study the quadrilateral. If it satisfies the properties, it is a parallelogram.)
- yes; Consecutive angles are not congruent. (Using the properties of parallelograms, study the quadrilateral. If it satisfies the properties, it is a parallelogram.)
- no; Consecutive angles are not congruent. (Using the properties of parallelograms, study the quadrilateral. If it satisfies the properties, it is a parallelogram.)
- yes; Opposite angles are congruent. (Using the properties of parallelograms, study the quadrilateral. If it satisfies the properties, it is a parallelogram.)
A: yes; Opposite angles are congruent.

Q: Determine whether the quadrilateral is a parallelogram. Justify your answer.

[Image]
- yes; Consecutive angles are not congruent. (Using the properties of parallelograms, study the quadrilateral. If it satisfies the properties, it is a parallelogram.)
- no; Consecutive angles are congruent. (Using the properties of parallelograms, study the quadrilateral. If it satisfies the properties, it is a parallelogram.)
- no; Opposite angles are not congruent. (Using the properties of parallelograms, study the quadrilateral. If it satisfies the properties, it is a parallelogram.)
- yes; Opposite angles are not congruent. (Using the properties of parallelograms, study the quadrilateral. If it satisfies the properties, it is a parallelogram.)
A: no; Opposite angles are not congruent.

Q: Determine whether a figure with the given vertices is a parallelogram. Use the method indicated.

[Image], [Image], [Image], [Image]; Slope Formula
- yes; The opposite sides have the same slope. (Using the method indicated, determine if the points form a parallelogram. If the opposite sides are congruent, the slopes of opposite sides are congruent, or the diagonals share the same midpoint, then the points form a parallelogram.)
- no; Opposite sides are the same length. (Using the method indicated, determine if the points form a parallelogram. If the opposite sides are congruent, the slopes of opposite sides are congruent, or the diagonals share the same midpoint, then the points form a parallelogram.)
- no; The opposite sides have the same slope. (Using the method indicated, determine if the points form a parallelogram. If the opposite sides are congruent, the slopes of opposite sides are congruent, or the diagonals share the same midpoint, then the points form a parallelogram.)
- yes; Opposite sides are the same length. (Using the method indicated, determine if the points form a parallelogram. If the opposite sides are congruent, the slopes of opposite sides are congruent, or the diagonals share the same midpoint, then the points form a parallelogram.)
A: yes; The opposite sides have the same slope.

Q: Determine whether a figure with the given vertices is a parallelogram. Use the method indicated.

[Image], [Image], [Image], [Image]; Distance and Slope Formulas
- no; The opposite sides are not congruent and do not have the same slope. (Using the method indicated, determine if the points form a parallelogram. If the opposite sides are congruent, the slopes of opposite sides are congruent, or the diagonals share the same midpoint, then the points form a parallelogram.)
- yes; The opposite sides do not have the same slope. (Using the method indicated, determine if the points form a parallelogram. If the opposite sides are congruent, the slopes of opposite sides are congruent, or the diagonals share the same midpoint, then the points form a parallelogram.)
- no; The opposite sides do not have the same slope. (Using the method indicated, determine if the points form a parallelogram. If the opposite sides are congruent, the slopes of opposite sides are congruent, or the diagonals share the same midpoint, then the points form a parallelogram.)
- yes; The opposite sides are not congruent and do not have the same slope. (Using the method indicated, determine if the points form a parallelogram. If the opposite sides are congruent, the slopes of opposite sides are congruent, or the diagonals share the same midpoint, then the points form a parallelogram.)
A: no; The opposite sides are not congruent and do not have the same slope.

Q: Quadrilateral ABCD is a rectangle.
[Image]

If [Image] and [Image], find [Image].
- 96 (The diagonals of a rectangle are congruent. Set the segments equal to each other and solve for the variable. Use the variable’s value to solve for the diagonal length.)
- –6 (The diagonals of a rectangle are congruent. Set the segments equal to each other and solve for the variable. Use the variable’s value to solve for the diagonal length.)
- 24 (The diagonals of a rectangle are congruent. Set the segments equal to each other and solve for the variable. Use the variable’s value to solve for the diagonal length.)
- 48 (The diagonals of a rectangle are congruent. Set the segments equal to each other and solve for the variable. Use the variable’s value to solve for the diagonal length.)
A: 96

Q: Quadrilateral ABCD is a rectangle.
[Image]

If [Image] and [Image], find [Image].
- 48 (Each angle of a rectangle is a right angle. Add the given angles together and set the sum equal to 90. Solve for the variable. Use the value of the variable to find the missing angle.)
- 1 (Each angle of a rectangle is a right angle. Add the given angles together and set the sum equal to 90. Solve for the variable. Use the value of the variable to find the missing angle.)
- 42 (Each angle of a rectangle is a right angle. Add the given angles together and set the sum equal to 90. Solve for the variable. Use the value of the variable to find the missing angle.)
- 45 (Each angle of a rectangle is a right angle. Add the given angles together and set the sum equal to 90. Solve for the variable. Use the value of the variable to find the missing angle.)
A: 42

Q: [Image]
In rhombus YZAB, if [Image]12, find [Image].
- 24 (All sides of a rhombus are congruent.)
- 12 (All sides of a rhombus are congruent.)
- 6 (All sides of a rhombus are congruent.)
- [Image] (All sides of a rhombus are congruent.)
A: 12

Q: [Image]
In rhombus TUVW, if [Image], find [Image].
- 56 (The diagonals of a rhombus bisect the angles. Also, consecutive angles are supplementary.)
- 68 (The diagonals of a rhombus bisect the angles. Also, consecutive angles are supplementary.)
- 34 (The diagonals of a rhombus bisect the angles. Also, consecutive angles are supplementary.)
- 112 (The diagonals of a rhombus bisect the angles. Also, consecutive angles are supplementary.)
A: 56

Q: Given each set of vertices, determine whether parallelogram ABCD is a rhombus, a rectangle, or a square. List all that apply.

[Image], [Image], [Image], [Image]
- square; rectangle; rhombus (Plot the vertices on a coordinate plane. Determine if the diagonals are perpendicular. If so, the quadrilateral is either a rhombus or square. Use the distance formula to compare the lengths of the diagonals. If the diagonals are congruent and perpendicular, the quadrilateral is a square.)
- rhombus (Plot the vertices on a coordinate plane. Determine if the diagonals are perpendicular. If so, the quadrilateral is either a rhombus or square. Use the distance formula to compare the lengths of the diagonals. If the diagonals are congruent and perpendicular, the quadrilateral is a square.)
- square (Plot the vertices on a coordinate plane. Determine if the diagonals are perpendicular. If so, the quadrilateral is either a rhombus or square. Use the distance formula to compare the lengths of the diagonals. If the diagonals are congruent and perpendicular, the quadrilateral is a square.)
- rectangle (Plot the vertices on a coordinate plane. Determine if the diagonals are perpendicular. If so, the quadrilateral is either a rhombus or square. Use the distance formula to compare the lengths of the diagonals. If the diagonals are congruent and perpendicular, the quadrilateral is a square.)
A: square; rectangle; rhombus

Q: Given each set of vertices, determine whether parallelogram ABCD is a rhombus, a rectangle, or a square. List all that apply.

[Image], [Image], [Image], [Image]
- rhombus (Plot the vertices on a coordinate plane. Determine if the diagonals are perpendicular. If so, the quadrilateral is either a rhombus or square. Use the distance formula to compare the lengths of the diagonals. If the diagonals are congruent and perpendicular, the quadrilateral is a square.)
- square; rectangle; rhombus (Plot the vertices on a coordinate plane. Determine if the diagonals are perpendicular. If so, the quadrilateral is either a rhombus or square. Use the distance formula to compare the lengths of the diagonals. If the diagonals are congruent and perpendicular, the quadrilateral is a square.)
- square (Plot the vertices on a coordinate plane. Determine if the diagonals are perpendicular. If so, the quadrilateral is either a rhombus or square. Use the distance formula to compare the lengths of the diagonals. If the diagonals are congruent and perpendicular, the quadrilateral is a square.)
- rectangle (Plot the vertices on a coordinate plane. Determine if the diagonals are perpendicular. If so, the quadrilateral is either a rhombus or square. Use the distance formula to compare the lengths of the diagonals. If the diagonals are congruent and perpendicular, the quadrilateral is a square.)
A: square; rectangle; rhombus

Q: For trapezoid JKLM, A and B are midpoints of the legs. Find ML.
[Image]
- 65 (To find the other base, substitute the given values into the formula [Image].)
- 32.5 (To find the other base, substitute the given values into the formula [Image].)
- 28 (To find the other base, substitute the given values into the formula [Image].)
- 3 (To find the other base, substitute the given values into the formula [Image].)
A: 28

Q: For trapezoid JKLM, A and B are midpoints of the legs. Find ML.
[Image]
- 4 (To find the other base, substitute the given values into the formula [Image].)
- 34 (To find the other base, substitute the given values into the formula [Image].)
- 68 (To find the other base, substitute the given values into the formula [Image].)
- 40 (To find the other base, substitute the given values into the formula [Image].)
A: 40

Q: For trapezoid JKLM, A and B are midpoints of the legs. Find AB.
[Image]
- 23 (To find the median, find the sum of the bases and then divide by two.)
- 8 (To find the median, find the sum of the bases and then divide by two.)
- 35 (To find the median, find the sum of the bases and then divide by two.)
- 46 (To find the median, find the sum of the bases and then divide by two.)
A: 23

Q: For trapezoid ABCD, E and F are midpoints of the legs. Let GH be the median of ABFE.
Find GH.
[Image]
- 7 (To find the median, find the sum of the bases and then divide by two.)
- 8 (To find the median, find the sum of the bases and then divide by two.)
- 4 (To find the median, find the sum of the bases and then divide by two.)
- 6 (To find the median, find the sum of the bases and then divide by two.)
A: 6

Q: Position and label each quadrilateral on the coordinate plane.

rectangle with side length b units and height d units
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
A: [Image]

Q: Position and label each quadrilateral on the coordinate plane.

square with side length b units
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
A: [Image]

Q: Position and label each quadrilateral on the coordinate plane.

trapezoid with height d units, bases b and [Image] units
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
A: [Image]

Q: Position and label each quadrilateral on the coordinate plane.

parallelogram with side length d units and height b units
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
A: [Image]

Q: Position and label each quadrilateral on the coordinate plane.

rectangle with side length 2k units and height 4k
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
A: [Image]

Q: Position and label each quadrilateral on the coordinate plane.

square with side length 4k units
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
A: [Image]

Q: Position and label each quadrilateral on the coordinate plane.

rectangle with side length 4k units and height 2k units
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
A: [Image]

Q: Position and label each quadrilateral on the coordinate plane.

square with side length 2k units
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
A: [Image]

Q: isosceles trapezoid with height c units, bases 4d units and 2d units
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
A: [Image]

Q: isosceles trapezoid with height c units, bases 8d units and 4d units
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
- [Image] (What are the properties of the given shape? Use the properties to determine what the graph should resemble.)
A: [Image]

Determine the relationship among EBHJ, JHCF, GJFD, and AEJG if ABCD is a parallelogram with E, J, and F the midpoints of [Image], [Image], and [Image] respectively, and G, J, and H the midpoints of [Image], [Image], and [Image] respectively.
[Image]

Determine the relationship between QJLK and JKLR if [Image] is equilateral and J, K, and L are midpoints of [Image], [Image], and [Image], respectively.
[Image]

Given: | JKLM is a rectangle. [Image]
Prove: | [Image]

[Image]

Given: | HJKL is a rectangle. M is the midpoint of [Image]
Prove: | [Image]

[Image]

Using the figure below, write a coordinate proof for the following condition.
The diagonals of a rectangle are congruent.
[Image]
[Image]

Using the figure below, write a coordinate proof for the following condition.
The diagonals of a rectangle are congruent.
[Image]
S (0, 0); P (0, b); Q (a, b); R (a, 0)

Using the figure below, write a coordinate proof for the following condition.
If the diagonals of a parallelogram are congruent, then it is a rectangle.
[Image]
R (0, 0); U (b, c); T (a + b, c); S (a, 0)

Using the figure below, write a coordinate proof for the following condition.
If the diagonals of a parallelogram are congruent, then it is a rectangle.
[Image]
[Image]

Using the figure below, write a coordinate proof for the following condition.
The diagonals of an isosceles trapezoid are congruent.
[Image]
D (0, 0); G (b, c); F (a – b, c); E (a, 0)

Using the figure below, write a coordinate proof for the following condition.
The diagonals of an isosceles trapezoid are congruent.
[Image]
[Image]

Using the figure below, write a coordinate proof for the following condition.
The diagonals of an isosceles trapezoid are congruent.
[Image]
U (b, 0); X (0, c); W (a, c); V (a – b, 0)

Using the figure below, write a coordinate proof for the following condition.
The median of a trapezoid is parallel to the bases.
[Image]
S (0, 0); P (–b, c); Q (a + b, c); R (a, 0)

Using the figure below, write a coordinate proof for the following condition.
The median of a trapezoid is parallel to the bases.
[Image]
[Image]

A park lodge is located next to a lake at point P. Kwan is standing 154 yards away at point Q. Dakota is standing 140 yards away from the other side of the lake at point S.
[Image]
a.      Explain why [Image] is similar to [Image].
b.      Write and solve a proportion to find the distance across the lake, k.

Parallelogram WXYZ has vertices with coordinates [Image], [Image], [Image], and [Image].
a.      If [Image], what can you determine about the slopes of the diagonals [Image]and [Image]?
b.      What kind of parallelogram is WXYZ?

Q: [Image: x =\underline{\;\;\;\;\;\;\;}, y =\underline{\;\;\;\;\;\;\;}]

[Image]
- x=57 y=123
- x=123 y=57
- x=57 y=57
- x=123 y=123
A: x=57 y=123

Q: [Image: w =\underline{\;\;\;\;\;\;\;}, z =\underline{\;\;\;\;\;\;\;}]

[Image]
- w=90 x=4
- w=90 z=9
- w=90 z=5
- w=9 z=13
A: w=90 z=9

Q: [Image: a =\underline{\;\;\;\;\;\;\;}, b =\underline{\;\;\;\;\;\;\;}]

[Image]
- a=83 b=91
- a=90 b=90
- a=97 b=89
- a=91 b=93
A: a=97 b=89

Q: [Image]
In rhombus YZAB, if [Image]2x-7, [Image]=3x-20. Solve for x.
- 27 (All sides of a rhombus are congruent.)
- 13 (All sides of a rhombus are congruent.)
- 12 (All sides of a rhombus are congruent.)
- 20 (All sides of a rhombus are congruent.)
A: 13

Q: [Image]
In rhombus YZAB, if [Image]4x+15, YB=2x+45. Find the length of YB.
- 15 (All sides of a rhombus are congruent.)
- 30 (All sides of a rhombus are congruent.)
- 75 (All sides of a rhombus are congruent.)
- 105 (All sides of a rhombus are congruent.)
A: 75

Q: [Image]
In rhombus YZAB, if [Image]7x+5, YB=4x+20. Find the length of AZ.
- 40 (All sides of a rhombus are congruent.)
- 5 (All sides of a rhombus are congruent.)
- 35 (All sides of a rhombus are congruent.)
- 10 (All sides of a rhombus are congruent.)
A: 40

Q: [Image]
In rhombus YZAB, if YO=10x-4, OA=6x+20. Solve for x.
- 4 (All sides of a rhombus are congruent.)
- 6 (All sides of a rhombus are congruent.)
- 56 (All sides of a rhombus are congruent.)
- 36 (All sides of a rhombus are congruent.)
A: 6