Worksheet: Relationships between Two Lines in Space

In this worksheet, we will practice identifying the relationships between two lines in three-dimensional figures.

Q1:

Using the cube below, decide which of the following describe the relative position of the straight lines 𝐴 𝐵 and 𝐷 𝐷 .

  • A intersecting
  • B parallel
  • C perpendicular
  • D skew

Q2:

Which of the following lists consists of three lines through the point 𝐴 ?

  • A 𝐴 𝐵 , 𝐵 𝐶 , 𝐴 𝐷
  • B 𝐴 𝐵 , 𝐴 𝐴 , 𝐴 𝐷
  • C 𝐴 𝐵 , 𝐴 𝐴 , 𝐴 𝐷

Q3:

Using the cube below, decide which of the following describe the relative position of the straight lines 𝐴 𝐶 and 𝐴 𝐶 .

  • A parallel
  • B skew
  • C perpendicular
  • D intersecting

Q4:

Using the cube below, decide which of the following describe the relative position of the straight lines 𝐴 𝐵 and 𝐷 𝐶 .

  • A intersecting
  • B skew
  • C perpendicular
  • D parallel

Q5:

Identify the missing phrase from the given sentence.

“Two lines, in the same plane, that do not intersect are said to be .

  • Aperpendicular lines
  • Bidentical lines
  • Cskew lines
  • Dparallel lines

Q6:

Consider the right pentagonal prism 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 𝐺 𝐻 𝐼 𝐽 .

What can be said about 𝐶 𝐷 and 𝐻 𝐼 ?

  • AThey are neither parallel nor perpendicular.
  • BThey are perpendicular.
  • CThey are skew.
  • DThey are parallel.

What can be said about 𝐴 𝐵 and 𝐵 𝐺 ?

  • AThey are skew.
  • BThey are neither parallel nor perpendicular.
  • CThey are parallel.
  • DThey are perpendicular.

What can be said about 𝐴 𝐷 and 𝐷 𝐼 ?

  • AThey are perpendicular.
  • BThey are parallel.
  • CThey are neither parallel nor perpendicular.
  • DThey are skew.

What can be said about 𝐷 𝐻 and 𝐶 𝐼 ?

  • AThey are neither parallel nor perpendicular.
  • BThey are skew.
  • CThey are parallel.
  • DThey are perpendicular.

Q7:

Consider the cuboid 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 𝐺 𝐻 , where 𝐴 𝐵 𝐵 𝐶 𝐴 𝐸 .

What can be said about 𝐸 𝐹 and 𝐹 𝐺 ?

  • AThey are neither parallel nor perpendicular.
  • BThey are parallel.
  • CThey are skew.
  • DThey are perpendicular.

What can be said about 𝐴 𝐸 and 𝐶 𝐺 ?

  • AThey are skew.
  • BThey are neither parallel nor perpendicular.
  • CThey are perpendicular.
  • DThey are parallel.

What can be said about 𝐵 𝐷 and 𝐷 𝐻 ?

  • AThey are perpendicular.
  • BThey are parallel.
  • CThey are neither parallel nor perpendicular.
  • DThey are skew.

What can be said about 𝐵 𝐷 and 𝐴 𝐶 ?

  • AThey are neither parallel nor perpendicular.
  • BThey are skew.
  • CThey are parallel.
  • DThey are perpendicular.

Q8:

Using the rectangular prism below, decide which of the following is skew to 𝐶 𝐺 .

  • A 𝐷 𝐶
  • B 𝐻 𝐺
  • C 𝐹 𝐵
  • D 𝐸 𝐻
  • E 𝐶 𝐵

Q9:

Complete: Two intersecting lines make angles.

  • A5
  • B2
  • C3
  • D4

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