Question

pre - algebra name ___ period ___ geometry unit 4 - parallel, perpendicular, skew lines use the diagram below to find the following: 1) a line parallel to nr. 2) a line skew to nr. 3) a line perpendicular to nr. 4) a pair of skew lines. 5) a pair of parallel sides.

Explanation:

Step1: Recall parallel - line definition

Parallel lines are lines in the same plane that never intersect. In a cube, edges on the same - face or corresponding edges of parallel faces are parallel. For a line parallel to NR, lines such as MQ, PO are parallel to NR as they have the same direction and will never intersect NR. Let's assume we choose MQ.

Step2: Recall skew - line definition

Skew lines are non - parallel and non - intersecting lines in 3 - D space. For a line skew to NR, consider MP. MP and NR are not in the same plane, they are not parallel, and they do not intersect.

Step3: Recall perpendicular - line definition

Perpendicular lines intersect at a right angle. Lines such as RN and NS are perpendicular to NR as they meet NR at a 90 - degree angle.

Step4: Recall pair of skew lines

A pair of skew lines could be MP and NR as explained above.

Step5: Recall pair of parallel sides

In the cube, for example, sides MQ and NR are a pair of parallel sides.

Answer:

1. MQ (a line parallel to NR)
2. MP (a line skew to NR)
3. RN (a line perpendicular to NR)
4. MP and NR (a pair of skew lines)
5. MQ and NR (a pair of parallel sides)