Question

pre - algebra
name tripp
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.

in the 3 - d figure above, which line is parallel to line qt?
a. line st
b. line qr
c. line rs
d. line mn
in the 3 - d figure above, which line is skew to line pt?
a. line mq
b. line no

Explanation:

Step1: Recall parallel lines definition

Parallel lines in 3 - D are lines in the same plane that do not intersect. In a rectangular prism, edges that are in the same - type of face and do not cross are parallel. For a line parallel to NR, we look for a line in the same - orientation in a parallel face. Line MQ is parallel to NR as they are in parallel rectangular faces and have the same direction.

Step2: Recall skew lines definition

Skew lines are lines that are not in the same plane and do not intersect. For a line skew to NR, we consider lines that are not in the planes containing NR. Line PO is skew to NR since they are not in the same plane and do not intersect.

Step3: Recall perpendicular lines definition

Perpendicular lines intersect at a right - angle. Lines like NQ and NR intersect at a right - angle, so NQ is perpendicular to NR.

Step4: Find a pair of skew lines

Skew lines example: PT and OS. They are not in the same plane and do not intersect.

Step5: Find a pair of parallel sides

Parallel sides example: PQ and SR. They are opposite sides of a rectangular face and are parallel.
For the multiple - choice part:

For the line parallel to QT

Lines in a rectangular prism that are parallel to a given edge are those in parallel faces with the same orientation. Line MN is parallel to QT as they are in parallel rectangular faces and have the same direction.

For the line skew to PT

Skew lines are non - coplanar non - intersecting lines. Line NO is skew to PT as they are not in the same plane and do not intersect.

Answer:

1. MQ
2. PO
3. NQ
4. PT and OS
5. PQ and SR

Multiple - choice:

• Which line is parallel to QT: D. line MN
• Which line is skew to PT: B. line NO