Title: Parallel and Perpendicular Lines
Course: quiz duplicate error

Q: Refer to the figure below.
[Image]

Name all planes intersecting plane [Image].
- [Image] (Make sure to find all four planes that intersect the given plane. One of the planes you listed might be a duplicate.)
- [Image] (Planes intersect in a line.)
- [Image] (Make sure to find all four planes that intersect the given plane. One of the planes you listed might be a duplicate.)
- [Image] (Make sure to find all four planes that intersect the given plane. One of the planes you listed might be a duplicate.)
A: [Image]

Q: Identify the sets of lines to which the given line is a transversal.

line i
[Image]
- m and p¸ n and o (A line that intersects two or more lines in a plane at different points is called a transversal.)
- m and n¸ n and o¸ m and o (A line that intersects two or more lines in a plane at different points is called a transversal.)
- j (A line that intersects two or more lines in a plane at different points is called a transversal.)
- m and n¸ n and o¸ m and o¸ m and p¸ n and p¸ o and p (A line that intersects two or more lines in a plane at different points is called a transversal.)
A: m and n¸ n and o¸ m and o¸ m and p¸ n and p¸ o and p

Q: Identify the sets of lines to which the given line is a transversal.

line a
[Image]
- c and b¸ f and d¸ c and f¸ c and d¸ b and d (A line that intersects two or more lines in a plane at different points is called a transversal.)
- a and b¸ a and c¸ a and d¸ a and f (A line that intersects two or more lines in a plane at different points is called a transversal.)
- f and d¸ c and f¸ c and d¸ b and d (A line that intersects two or more lines in a plane at different points is called a transversal.)
- c and b¸ f and d (A line that intersects two or more lines in a plane at different points is called a transversal.)
A: c and b¸ f and d¸ c and f¸ c and d¸ b and d

Q: Refer to the figure below.
[Image]

Name all planes intersecting plane [Image].
- [Image] (Make sure to find all four planes that intersect the given plane. One of the planes you listed might be a duplicate.)
- [Image] (Planes intersect in a line.)
- [Image] (Make sure to find all four planes that intersect the given plane. One of the planes you listed might be a duplicate.)
- [Image] (Make sure to find all four planes that intersect the given plane. One of the planes you listed might be a duplicate.)
A: [Image]
Feedback: Make sure to find all four planes that intersect the given plane. One of the planes you listed might be a duplicate.

Q: Refer to the figure below.
[Image]

Name all planes intersecting plane CDI.
- ABC, CBG, ADI, FGH (Planes that intersect have a common line.)
- CBA, DAF, HGF (Planes that intersect have a common line.)
- BAD, GFI, CBG, GFA (Planes that intersect have a common line.)
- DAB, CBG, FAD (Planes that intersect have a common line.)
A: ABC, CBG, ADI, FGH / CBA, DAF, HGF / BAD, GFI, CBG, GFA / DAB, CBG, FAD

Q: Refer to the figure below.
[Image]

Name all segments skew to [Image].
- [Image] (Skew lines do not intersect and are not coplanar.)
- [Image] (Skew lines do not intersect and are not coplanar.)
- [Image] (Skew lines do not intersect and are not coplanar.)
- [Image] (Skew lines do not intersect and are not coplanar.)
A: [Image]

Q: Refer to the figure below.
[Image]

Name all segments parallel to [Image].
- [Image] (Coplanar segments that do not intersect are parallel.)
- [Image] (Coplanar segments that do not intersect are parallel.)
- [Image] (Coplanar segments that do not intersect are parallel.)
- [Image] (Coplanar segments that do not intersect are parallel.)
A: [Image]

Q: Determine the slope of the line that contains the given points.

[Image]
- [Image] (The formula for slope is [Image].)
- [Image] (The formula for slope is [Image].)
- [Image] (The formula for slope is [Image].)
- [Image] (The formula for slope is [Image].)
A: [Image]

Q: Write an equation in point-slope form of the line having the given slope that contains the given point.

[Image]
- [Image] (The point-slope form is [Image]. Point [Image] is a point through which the line passes.)
- [Image] (The point-slope form is [Image]. Point [Image] is a point through which the line passes.)
- [Image] (The point-slope form is [Image]. Point [Image] is a point through which the line passes.)
- [Image] (The point-slope form is [Image]. Point [Image] is a point through which the line passes.)
A: [Image]

Q: In the figure, [Image], [Image]and [Image]. Find the measure of angle PRK.
[Image]
- 120 (Corresponding angles are congruent. Alternate interior angles are congruent. Consecutive interior angles are supplementary. Alternate exterior angles are congruent.)
- 60 (Corresponding angles are congruent. Alternate interior angles are congruent. Consecutive interior angles are supplementary. Alternate exterior angles are congruent.)
- 100 (Corresponding angles are congruent. Alternate interior angles are congruent. Consecutive interior angles are supplementary. Alternate exterior angles are congruent.)
- 40 (Corresponding angles are congruent. Alternate interior angles are congruent. Consecutive interior angles are supplementary. Alternate exterior angles are congruent.)
A: 120

Q: In the figure, [Image] and [Image]. Find the measure of angle WSP.
[Image]
- 85 (Corresponding angles are congruent. Alternate interior angles are congruent. Consecutive interior angles are supplementary. Alternate exterior angles are congruent.)
- 75 (Corresponding angles are congruent. Alternate interior angles are congruent. Consecutive interior angles are supplementary. Alternate exterior angles are congruent.)
- 95 (Corresponding angles are congruent. Alternate interior angles are congruent. Consecutive interior angles are supplementary. Alternate exterior angles are congruent.)
- 65 (Corresponding angles are congruent. Alternate interior angles are congruent. Consecutive interior angles are supplementary. Alternate exterior angles are congruent.)
A: 85

Q: Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer.

[Image]
[Image]
- [Image]; congruent corresponding angles (Postulates and theorems: If corresponding angles are congruent, then lines are parallel. If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line. If alternate exterior angles are congruent, then lines are parallel. If consecutive interior angles are supplementary, then lines are parallel. If alternate interior angles are congruent, then lines are parallel. If 2 lines are perpendicular to the same line, then lines are parallel.)
- [Image]; congruent corresponding angles (Postulates and theorems: If corresponding angles are congruent, then lines are parallel. If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line. If alternate exterior angles are congruent, then lines are parallel. If consecutive interior angles are supplementary, then lines are parallel. If alternate interior angles are congruent, then lines are parallel. If 2 lines are perpendicular to the same line, then lines are parallel.)
- [Image]; congruent alternate interior angles (Postulates and theorems: If corresponding angles are congruent, then lines are parallel. If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line. If alternate exterior angles are congruent, then lines are parallel. If consecutive interior angles are supplementary, then lines are parallel. If alternate interior angles are congruent, then lines are parallel. If 2 lines are perpendicular to the same line, then lines are parallel.)
- [Image]; congruent alternate interior angles (Postulates and theorems: If corresponding angles are congruent, then lines are parallel. If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line. If alternate exterior angles are congruent, then lines are parallel. If consecutive interior angles are supplementary, then lines are parallel. If alternate interior angles are congruent, then lines are parallel. If 2 lines are perpendicular to the same line, then lines are parallel.)
A: [Image]; congruent alternate interior angles

Q: Find the distance between the pair of parallel lines.

[Image]
- [Image] (The slope of a line perpendicular to each has the negative reciprocal to the equation of one of the lines. The perpendicular line containing the y-intercept would be [Image]. You need to find a common point for the two lines so set the equations equal to each other. [Image] Use the Distance Formula from that common point to the y-intercept of the first line: [Image])
- [Image] (The slope of a line perpendicular to each has the negative reciprocal to the equation of one of the lines. The perpendicular line containing the y-intercept would be [Image]. You need to find a common point for the two lines so set the equations equal to each other. [Image] Use the Distance Formula from that common point to the y-intercept of the first line: [Image])
- [Image] (The slope of a line perpendicular to each has the negative reciprocal to the equation of one of the lines. The perpendicular line containing the y-intercept would be [Image]. You need to find a common point for the two lines so set the equations equal to each other. [Image] Use the Distance Formula from that common point to the y-intercept of the first line: [Image])
- [Image] (The slope of a line perpendicular to each has the negative reciprocal to the equation of one of the lines. The perpendicular line containing the y-intercept would be [Image]. You need to find a common point for the two lines so set the equations equal to each other. [Image] Use the Distance Formula from that common point to the y-intercept of the first line: [Image])
A: [Image]

Q: Write an equation in slope-intercept form of the line having the given slope and y-intercept.

[Image]
- [Image] (The slope-intercept form is [Image]. Point b is the point at which [Image].)
- [Image] (The slope-intercept form is [Image]. Point b is the point at which [Image].)
- [Image] (The slope-intercept form is [Image]. Point b is the point at which [Image].)
- [Image] (The slope-intercept form is [Image]. Point b is the point at which [Image].)
A: [Image]

Q: Write an equation in slope-intercept form of the line having the given slope and y-intercept.

[Image]
- [Image] (The slope-intercept form is [Image].)
- [Image] (The slope-intercept form is [Image].)
- [Image] (The slope-intercept form is [Image].)
- [Image] (The slope-intercept form is [Image].)
A: [Image]

Q: Determine whether [Image] and [Image] are parallel, perpendicular, or neither.

[Image]
- parallel (The formula for slope is [Image]. If the slopes are the same they are parallel. If the product of the two slopes is –1, they are perpendicular.)
- perpendicular (The formula for slope is [Image]. If the slopes are the same they are parallel. If the product of the two slopes is –1, they are perpendicular.)
- neither (The formula for slope is [Image]. If the slopes are the same they are parallel. If the product of the two slopes is –1, they are perpendicular.)
A: neither

Q: Construct a line perpendicular to m through P. Then find the distance from P to m.

Line m contains points [Image] and [Image]. Point P has coordinates [Image].
- [Image] [Image] (The slope of a line p perpendicular to m has the negative reciprocal to the equation of line m. The slope of line m is [Image], which is 0. This is a horizontal line. The perpendicular line, then would be a vertical line, [Image], going through point P. The point on m where line p intersects it would be [Image]. Use the Distance Formula to find the distance from point P to the point on m that intersects line p: [Image])
- [Image] [Image] (The slope of a line p perpendicular to m has the negative reciprocal to the equation of line m. The slope of line m is [Image], which is 0. This is a horizontal line. The perpendicular line, then would be a vertical line, [Image], going through point P. The point on m where line p intersects it would be [Image]. Use the Distance Formula to find the distance from point P to the point on m that intersects line p: [Image])
- [Image] [Image] (The slope of a line p perpendicular to m has the negative reciprocal to the equation of line m. The slope of line m is [Image], which is 0. This is a horizontal line. The perpendicular line, then would be a vertical line, [Image], going through point P. The point on m where line p intersects it would be [Image]. Use the Distance Formula to find the distance from point P to the point on m that intersects line p: [Image])
- [Image] [Image] (The slope of a line p perpendicular to m has the negative reciprocal to the equation of line m. The slope of line m is [Image], which is 0. This is a horizontal line. The perpendicular line, then would be a vertical line, [Image], going through point P. The point on m where line p intersects it would be [Image]. Use the Distance Formula to find the distance from point P to the point on m that intersects line p: [Image])
A: [Image] [Image]

Q: In the figure, [Image]. Find [Image].
[Image]
- [Image] (Extend v to intersect with p. This creates a linear pair at point S with angles measuring [Image]° (given) and 61°. The angles formed by the intersection of v and p (also linear pairs) measure [Image]° (corresponding angles) and 55° with the latter being one of the interior angles of the triangle formed by t, p and v. Since the sum of the angles of a triangle is 180°, the angle that is vertical to <1 is 64°, thus making <1 64° as well.)
- [Image] (Extend v to intersect with p. This creates a linear pair at point S with angles measuring [Image]° (given) and 61°. The angles formed by the intersection of v and p (also linear pairs) measure [Image]° (corresponding angles) and 55° with the latter being one of the interior angles of the triangle formed by t, p and v. Since the sum of the angles of a triangle is 180°, the angle that is vertical to <1 is 64°, thus making <1 64° as well.)
- [Image] (Extend v to intersect with p. This creates a linear pair at point S with angles measuring [Image]° (given) and 61°. The angles formed by the intersection of v and p (also linear pairs) measure [Image]° (corresponding angles) and 55° with the latter being one of the interior angles of the triangle formed by t, p and v. Since the sum of the angles of a triangle is 180°, the angle that is vertical to <1 is 64°, thus making <1 64° as well.)
- [Image] (Extend v to intersect with p. This creates a linear pair at point S with angles measuring [Image]° (given) and 61°. The angles formed by the intersection of v and p (also linear pairs) measure [Image]° (corresponding angles) and 55° with the latter being one of the interior angles of the triangle formed by t, p and v. Since the sum of the angles of a triangle is 180°, the angle that is vertical to <1 is 64°, thus making <1 64° as well.)
A: [Image]

Q: Construct a line perpendicular to m through P. Then find the distance from P to m.

Line m contains points [Image] and [Image]. Point P has coordinates [Image].
- [Image] [Image] (The slope of line m is [Image], which is [Image]. The equation for line m is [Image] or [Image]. The slope of a line p perpendicular to m has the negative reciprocal to the equation of line m. The perpendicular line, then would be [Image], going through point P. The line containing point P would be [Image] or [Image]. You need to find a common point for the two lines so set the equations equal to each other. [Image] Use the Distance Formula from that common point to point P: [Image])
- [Image] [Image] (The slope of line m is [Image], which is [Image]. The equation for line m is [Image] or [Image]. The slope of a line p perpendicular to m has the negative reciprocal to the equation of line m. The perpendicular line, then would be [Image], going through point P. The line containing point P would be [Image] or [Image]. You need to find a common point for the two lines so set the equations equal to each other. [Image] Use the Distance Formula from that common point to point P: [Image])
- [Image] [Image] (The slope of line m is [Image], which is [Image]. The equation for line m is [Image] or [Image]. The slope of a line p perpendicular to m has the negative reciprocal to the equation of line m. The perpendicular line, then would be [Image], going through point P. The line containing point P would be [Image] or [Image]. You need to find a common point for the two lines so set the equations equal to each other. [Image] Use the Distance Formula from that common point to point P: [Image])
- [Image] [Image] (The slope of line m is [Image], which is [Image]. The equation for line m is [Image] or [Image]. The slope of a line p perpendicular to m has the negative reciprocal to the equation of line m. The perpendicular line, then would be [Image], going through point P. The line containing point P would be [Image] or [Image]. You need to find a common point for the two lines so set the equations equal to each other. [Image] Use the Distance Formula from that common point to point P: [Image])
A: [Image] [Image]

Q: Determine whether [Image] and [Image] are parallel, perpendicular, or neither.

[Image]
- perpendicular (The formula for slope is [Image]. If the slopes are the same they are parallel. If the product of the two slopes is –1, they are perpendicular.)
- parallel (The formula for slope is [Image]. If the slopes are the same they are parallel. If the product of the two slopes is –1, they are perpendicular.)
- neither (The formula for slope is [Image]. If the slopes are the same they are parallel. If the product of the two slopes is –1, they are perpendicular.)
A: neither

Q: In the figure, [Image]. Find x and y.
[Image]
- [Image] (Corresponding angles are congruent. Alternate interior angles are congruent. Consecutive interior angles are supplementary. Alternate exterior angles are congruent.)
- [Image] (Corresponding angles are congruent. Alternate interior angles are congruent. Consecutive interior angles are supplementary. Alternate exterior angles are congruent.)
- [Image] (Corresponding angles are congruent. Alternate interior angles are congruent. Consecutive interior angles are supplementary. Alternate exterior angles are congruent.)
- [Image] (Corresponding angles are congruent. Alternate interior angles are congruent. Consecutive interior angles are supplementary. Alternate exterior angles are congruent.)
A: [Image]

Q: Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer.

[Image]
[Image]
- [Image]; congruent corresponding angles (Postulates and theorems: If corresponding angles are congruent, then lines are parallel. If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line. If alternate exterior angles are congruent, then lines are parallel. If consecutive interior angles are supplementary, then lines are parallel. If alternate interior angles are congruent, then lines are parallel. If 2 lines are perpendicular to the same line, then lines are parallel.)
- [Image]; congruent corresponding angles (Postulates and theorems: If corresponding angles are congruent, then lines are parallel. If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line. If alternate exterior angles are congruent, then lines are parallel. If consecutive interior angles are supplementary, then lines are parallel. If alternate interior angles are congruent, then lines are parallel. If 2 lines are perpendicular to the same line, then lines are parallel.)
- [Image]; congruent alternate exterior angles (Postulates and theorems: If corresponding angles are congruent, then lines are parallel. If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line. If alternate exterior angles are congruent, then lines are parallel. If consecutive interior angles are supplementary, then lines are parallel. If alternate interior angles are congruent, then lines are parallel. If 2 lines are perpendicular to the same line, then lines are parallel.)
- [Image]; congruent alternate exterior angles (Postulates and theorems: If corresponding angles are congruent, then lines are parallel. If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line. If alternate exterior angles are congruent, then lines are parallel. If consecutive interior angles are supplementary, then lines are parallel. If alternate interior angles are congruent, then lines are parallel. If 2 lines are perpendicular to the same line, then lines are parallel.)
A: [Image]; congruent alternate exterior angles

Write a two-column proof of the theorem.

If [Image], then [Image].
[Image]

Regina, age 10, is a fullback, or defender, for her soccer team. She kicked the ball from the corner of the sideline and the halfway line (denoted by the A below ) hard enough to go 120 ft. toward the forward (denoted by B) so the forward could take a shot on goal. Did her kick reach the forward? Explain and show your calculations to justify your answer.
[Image]

The Widget Company has been making their product and selling it to the public since 1996. They have raised the price of their product 5% of the initial price each year since the company started. The initial price was $49.00 in 1996.

a.      Graph the product’s cost from 1996 through 2004.
b.      If the pricing trend continues, what should the company charge for their product in 2007? Show your work.
c.      If the company charges $71 in 2005, does that keep with the trend? If not, how much should the company raise or lower their price to meet the trend? Show your work.