Worksheet: Points, Lines, and Planes in Space

In this worksheet, we will practice identifying and modeling geometric concepts like points, lines, and planes in space along with their properties.

Q1:

State whether the following is true or false: Two coplanar lines perpendicular to the same line will always intersect each other.

  • Afalse
  • Btrue

Q2:

Complete the following: Two skew lines are two lines that .

  • Alie in the same plane and do not have a common point
  • Bintersect but do not lie in the same plane
  • Care parallel
  • Ddo not lie in the same plane and do not intersect
  • Elie in the same plane and have a common point

Q3:

How many planes can pass through three non-collinear points?

  • A1
  • Ban infinite number
  • C2
  • D3

Q4:

In what line do planes 𝛼 and 𝑄𝑅𝑉 intersect?

  • A 𝑉 𝑁
  • B 𝑆 𝑅
  • C 𝑄 𝑅
  • D 𝑁 𝑄
  • E 𝑅 𝑉

Q5:

What is the intersection of the plane through 𝐴𝐵𝐵𝐴 and the plane through 𝐵𝐶𝐶𝐵?

  • A 𝐵 𝐵
  • B
  • C 𝐴 𝐵
  • D 𝐴 𝐵

Q6:

Complete the following: Two intersecting lines are two lines that .

  • Ado not lie in the same plane
  • Blie in the same plane and do not have a common point
  • Clie in the same plane and have a common point
  • Dare perpendicular
  • Eare parallel

Q7:

What is the intersection of planes 𝑀𝐴𝐵, 𝑀𝐵𝐶, and 𝑀𝐴𝐶?

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

Q8:

What is the intersection between segment 𝐵𝐵 and the plane 𝐴𝐵𝐶?

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

Q9:

What is the intersection of the planes 𝑀𝐴𝐵 and 𝑀𝐵𝐶?

  • A 𝐴 𝐶
  • B 𝑀 𝐵
  • Cthe plane 𝐴𝐵𝐶
  • Dthe plane 𝑀𝐴𝐶

Q10:

Determine the intersection of plane 𝐷𝐶𝐶𝐷 and plane 𝐴𝐵𝐶𝐷 and plane 𝐴𝐷𝐷𝐴.

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

Q11:

Observe the following figure and choose.

  • AThe straight line is contained within the plane.
  • BThe straight line is intersected with the plane.
  • CThe straight line is parallel to the plane.

Q12:

Observe the following figure and choose.

  • AThe straight line is parallel to the plane.
  • BThe straight line is contained within the plane.
  • CThe straight line is intersected with the plane.

Q13:

𝑋 and 𝑌 are planes that intersect at line 𝐿. 𝐴 is a point on line 𝐿 and 𝐶 is a point on plane 𝑋. Which of the following are true?

  • A 𝐶 𝑌
  • B 𝐶 𝑌
  • C 𝐶 𝑌
  • D 𝐶 𝑋

Q14:

𝑋 and 𝑌 are planes that intersect at line 𝐿. 𝐴 and 𝐵 are points on line 𝐿 and 𝐶 is a point on plane 𝑋. Which of the following statements hold?

  • A 𝐵 𝐶 𝑌
  • B 𝐵 𝐶 𝑋
  • C 𝐵 𝐶 𝑌
  • D 𝐵 𝐶 𝑌

Q15:

𝑋 and 𝑌 are planes that intersect at line 𝐿. 𝐵 is a point on plane 𝑋 and 𝐶 is a point on plane 𝑌. Determine the intersection of plane 𝑌 with plane 𝐴𝐵𝐶.

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

Q16:

Complete: If 𝐿 is parallel to the plane 𝑋, then 𝐿𝑋=.

  • A 𝑋
  • B 𝐿
  • C

Q17:

Describe what is shown in the figure.

  • AA plane 𝐴𝐵𝐶 intersected by 𝐷𝐸
  • BA plane 𝐴𝐵𝐶 intersected by 𝐶𝐵
  • CA plane 𝐵𝐶𝐷 intersected by 𝐴𝐸

Q18:

There are two parallel planes, 𝐴𝐵𝐷 and 𝐸𝐹𝐺. A line 𝑙 intersects the planes 𝐴𝐵𝐷 and 𝐸𝐹𝐺 at points 𝐴 and 𝐺 respectively. The plane 𝐴𝐵𝐷 contains 𝐴𝐶. Which figure matches the description?

  • A
  • B
  • C

Q19:

Which of the following is a line containing the point 𝑌?

  • A 𝑇 𝑋
  • B 𝑇 𝑊
  • C 𝑉 𝑊
  • D 𝑋 𝑍
  • E 𝑉 𝑍

Q20:

Which of the following is a line containing the point 𝑇?

  • A 𝑊 𝑋
  • B 𝑉 𝑊
  • C 𝑇 𝑋
  • D 𝑌 𝑍
  • E 𝑊 𝑌

Q21:

Which of the following is a line containing the point 𝑋?

  • A 𝑇 𝑌
  • B 𝑋 𝑊
  • C 𝑇 𝑊
  • D 𝑊 𝑍
  • E 𝑌 𝑍

Q22:

Which of the following is a line containing the point 𝑊?

  • A 𝑇 𝑌
  • B 𝑉 𝑍
  • C 𝑇 𝑊
  • D 𝑌 𝑍
  • E 𝑉 𝑌

Q23:

Which of the following lines contains the point 𝑉?

  • A 𝑌 𝑍
  • B 𝑋 𝑊
  • C 𝑇 𝑊
  • D 𝑋 𝑍
  • E 𝑇 𝑌

Q24:

Consider the following figure.

Write another name for the plane 𝒫.

  • APlane 𝐷𝐸𝐹
  • BPlane 𝐴𝐵𝐸𝐷
  • CPlane 𝐴𝐵𝐶
  • DPlane 𝐴𝐶𝐹𝐷
  • EPlane 𝐵𝐶𝐹𝐸

How many planes are shown in the figure?

Which two planes intersect in 𝐴𝐷?

  • APlane 𝐴𝐶𝐹𝐷 and plane 𝐴𝐵𝐸𝐷
  • BPlane 𝐴𝐶𝐹𝐷 and plane 𝐴𝐵𝐶
  • CPlane 𝐴𝐶𝐹𝐷 and plane 𝐷𝐸𝐹
  • DPlane 𝐴𝐵𝐸𝐷 and plane 𝐷𝐸𝐹
  • EPlane 𝐴𝐵𝐶 and plane 𝐴𝐵𝐸𝐷

Are planes 𝒫 and 𝐷𝐸𝐹 parallel or intersecting?

  • AIt cannot be determined without more information.
  • BThey are intersecting.
  • CThey are parallel.

Q25:

𝑋 and 𝑌 are planes which intersect at line 𝐿. Which of the following holds?

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

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