Worksheet: Points, Lines, and Planes

In this worksheet, we will practice identifying and modeling geometric concepts like points, lines, and planes 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.

  • A false
  • B true

Q2:

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

  • A lie in the same plane and do not have a common point
  • B lie in the same plane and have a common point
  • C intersect but do not lie in the same plane
  • D do not lie in the same plane and do not intersect
  • E are parallel

Q3:

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

  • Aan infinite number
  • B2
  • C3
  • D1

Q4:

In what line do planes 𝛼 and 𝑄 𝑅 𝑉 intersect?

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

Q5:

What is the intersection of the plane through 𝐴 𝐵 𝐵 𝐴 and the plane through 𝐵 𝐶 𝐶 𝐵 ?

  • A 𝐴 𝐵
  • B 𝐴 𝐵
  • C
  • D 𝐵 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
  • Care parallel
  • Dlie in the same plane and have a common point
  • Eare perpendicular

Q7:

What is the intersection of planes 𝑀 𝐴 𝐵 , 𝑀 𝐵 𝐶 , and 𝑀 𝐴 𝐶 ?

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

Q8:

What is the intersection between segment 𝐵 𝐵 and the plane 𝐴 𝐵 𝐶 ?

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

Q9:

What is the intersection of the planes 𝑀 𝐴 𝐵 and 𝑀 𝐵 𝐶 ?

  • A the plane 𝑀 𝐴 𝐶
  • B 𝐴 𝐶
  • C the plane 𝐴 𝐵 𝐶
  • D 𝑀 𝐵

Q10:

Determine the intersection of plane 𝐷 𝐶 𝐶 𝐷 and plane 𝐴 𝐵 𝐶 𝐷 and plane 𝐴 𝐷 𝐷 𝐴 .

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

Q11:

Observe the following figure and choose.

  • A The straight line is contained within the plane.
  • B The straight line is parallel to the plane.
  • C The straight line is intersected with the plane.

Q12:

Observe the following figure and choose.

  • A The straight line is contained within the plane.
  • B The straight line is intersected with the plane.
  • C The straight line is parallel to 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 𝑋
  • C 𝐶 𝑌
  • D 𝐶 𝑌

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 𝑌
  • C 𝐵 𝐶 𝑋
  • 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 𝐴 𝐵 𝐶 .

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

Q16:

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

  • A 𝑋
  • B 𝐿
  • C

Q17:

Describe what is shown in the figure.

  • AA plane 𝐴 𝐵 𝐶 intersected by 𝐶 𝐵
  • BA plane 𝐵 𝐶 𝐷 intersected by 𝐴 𝐸
  • CA plane 𝐴 𝐵 𝐶 intersected by 𝐷 𝐸

Q18:

There are two parallel planes, 𝐴 𝐵 𝐷 and 𝐸 𝐹 𝐺 . A line 𝑙 intersects the planes 𝐴 𝐵 𝐷 and 𝐸 𝐹 𝐺 at points 𝐴 and 𝐺 respectively. The plane 𝐴 𝐵 𝐷 contains 𝐴 𝐶 . Which figure matches the description?

  • A
  • B
  • C

Q19:

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

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

Q20:

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

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

Q21:

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

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

Q22:

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

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

Q23:

Which of the following lines contains the point 𝑉 ?

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

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