Chapter 3 MidChapter Quiz

Plane ABE is parallel to plane CDF because both planes contain the same line segment AB. Two planes are parallel if they do not intersect and have no common points. Since both planes contain the same line segment, they do not intersect and are therefore parallel.

Segment AB is skew to segment GH. Skew lines are lines that do not intersect and are not parallel. In this case, segment AB and segment GH do not intersect, and they are not parallel to each other. Therefore, segment AB is skew to segment GH.

The special name for the angle pair ∠3 and ∠12 is "alternate exterior." Alternate exterior angles are a pair of angles that lie on opposite sides of the transversal and are outside the two intersected lines. In this case, ∠3 and ∠12 are alternate exterior angles because they are on opposite sides of the transversal and are outside the lines that they intersect.

The given statement p || r indicates that either p or r (or both) is true. Since m8 = 119, we can conclude that p is true. Therefore, m11 must be the next odd number after 119, which is 121. However, 121 is not one of the answer choices. The closest answer choice is 119, but that is not the correct answer. Therefore, the correct answer must be 61, as it is the only remaining option.

The special name for angle pairs that are in the same relative position on different lines is "corresponding". In this case, angle 2 and angle 4 are corresponding angles because they are on opposite sides of the transversal line and in the same position relative to the parallel lines.

To determine whether two lines are parallel, perpendicular, or neither, we can calculate the slopes of the lines. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1)/(x2 - x1).

Let's calculate the slopes of the lines AB and DF.
The slope of AB = (-9 - 6)/(2 - (-1)) = -15/3 = -5.
The slope of DF = (2 - (-1))/(5 - (-10)) = 3/15 = 1/5.

Since the slopes of AB and DF are negative reciprocals of each other (-5 and 1/5), the lines are perpendicular.

The given points A(-2, -11), B(6, 5), D(-7, -10), and F(2, 8) form two distinct lines. To determine if these lines are parallel, we can calculate the slopes of the two lines. The slope of the line passing through points A and B is (5 - (-11))/(6 - (-2)) = 16/8 = 2. The slope of the line passing through points D and F is (8 - (-10))/(2 - (-7)) = 18/9 = 2. Since the slopes of both lines are equal, we can conclude that the lines are parallel.

The slope of a line is a measure of how steep the line is. In this case, the slope of line m is -1/4. This means that for every 4 units we move horizontally along the line, we move 1 unit downward. The negative sign indicates that the line has a downward slope.

The slope of a line represents the rate at which the line rises or falls as it moves from left to right. In this case, the slope of line k is 1/2. This means that for every 1 unit the line moves to the right, it will rise 1/2 unit. The slope can also be interpreted as the ratio of the vertical change to the horizontal change between any two points on the line. Therefore, for every 2 units the line moves to the right, it will rise 1 unit.

The given answer states that the value of x is 28 and the value of y is 19. This means that in the given figure, the variable x is equal to 28 and the variable y is equal to 19.