Worksheet: Intersections of Lines and Planes

In this worksheet, we will practice identifying the relationships between lines and planes and finding the results of these intersections.

Q1:

In the following figure, determine the intersection of plane 𝐴 𝐷 𝐴 and plane 𝐵 𝐷 𝐵 .

  • A 𝐴 𝐵
  • B { 𝐷 }
  • C 𝐴 𝐵
  • D 𝐶 𝐶

Q2:

Which of the following statements is true about the two planes?

  • A The two planes are parallel.
  • B The two planes are coincident.
  • C The two planes are intersected.

Q3:

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

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

Q4:

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

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

Q5:

In the following figure, determine the intersection of plane 𝐴 𝐷 𝐵 and plane 𝐴 𝐵 𝐶 .

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

Q6:

In the following figure, determine the intersection of plane 𝐴 𝐷 𝐵 and plane 𝐵 𝐶 𝐶 𝐵 .

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

Q7:

Determine the intersection of plane X with plane ABC.

  • A 𝐴 𝐶
  • B 𝐿
  • C { 𝐴 }
  • D 𝐴 𝐵

Q8:

Find three planes that pass through both of the points 𝐵 and 𝐶 .

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

Q9:

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

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

Q10:

Which of the following is a plane that is parallel to 𝐴 𝐵 𝐶 𝐷 ?

  • A plane 𝐴 𝐵 𝐵 𝐴
  • B plane 𝐶 𝐷 𝐷 𝐶
  • C plane 𝐵 𝐶 𝐶 𝐵
  • D plane 𝐴 𝐵 𝐶 𝐷
  • E plane 𝐴 𝐷 𝐷 𝐴

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