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Worksheet: Points, Lines, and Planes

Q1:

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

Q2:

Consider the following figure.

Write another name for the plane 𝒫 .

  • APlane 𝐴 𝐡 𝐸 𝐷
  • BPlane 𝐷 𝐸 𝐹
  • CPlane 𝐴 𝐢 𝐹 𝐷
  • DPlane 𝐴 𝐡 𝐢
  • EPlane 𝐡 𝐢 𝐹 𝐸

How many planes are shown in the figure?

Which two planes intersect in 𝐴 𝐷 ?

  • APlane 𝐴 𝐢 𝐹 𝐷 and plane 𝐷 𝐸 𝐹
  • BPlane 𝐴 𝐢 𝐹 𝐷 and plane 𝐴 𝐡 𝐢
  • CPlane 𝐴 𝐢 𝐹 𝐷 and plane 𝐴 𝐡 𝐸 𝐷
  • DPlane 𝐴 𝐡 𝐢 and plane 𝐴 𝐡 𝐸 𝐷
  • EPlane 𝐴 𝐡 𝐸 𝐷 and plane 𝐷 𝐸 𝐹

Are planes 𝒫 and 𝐷 𝐸 𝐹 parallel or intersecting?

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

Q3:

𝑋 and π‘Œ are planes that intersect at line 𝐿 . 𝐴 is a point on line 𝐿 and 𝐢 is a point on plane 𝑋 . Which of the following are true?

  • A 𝐢 ∈ π‘Œ
  • B 𝐢 βˆ‰ 𝑋
  • C 𝐢 βŠ‚ π‘Œ
  • D 𝐢 βˆ‰ π‘Œ

Q4:

𝑋 and π‘Œ are planes that intersect at line 𝐿 . 𝐴 and 𝐡 are points on line 𝐿 and 𝐢 is a point on plane 𝑋 . Which of the following statements hold?

  • A βƒ–     βƒ— 𝐡 𝐢 ∈ π‘Œ
  • B βƒ–     βƒ— 𝐡 𝐢 βŠ‚ π‘Œ
  • C βƒ–     βƒ— 𝐡 𝐢 βˆ‰ 𝑋
  • D βƒ–     βƒ— 𝐡 𝐢 βŠ„ π‘Œ

Q5:

𝑋 and π‘Œ are planes that intersect at line 𝐿 . 𝐡 is a point on plane 𝑋 and 𝐢 is a point on plane π‘Œ . Determine the intersection of plane π‘Œ with plane 𝐴 𝐡 𝐢 .

  • A βƒ–     βƒ— 𝐴 𝐡
  • B βƒ– βƒ— 𝐿
  • C { 𝐴 }
  • D βƒ–     βƒ— 𝐴 𝐢

Q6:

𝑋 and π‘Œ are planes that intersect at line 𝐿 . 𝐴 is a point on line 𝐿 , 𝐢 is a point on plane π‘Œ and 𝐡 is a point on plane 𝑋 . Which of the following represent the intersection of plane 𝑋 , plane π‘Œ and plane 𝐴 𝐡 𝐢 ?

  • A βƒ–     βƒ— 𝐡 𝐢
  • B βƒ– βƒ— 𝐿
  • C βˆ…
  • D { 𝐴 }

Q7:

Which of the following is a line containing the point π‘Œ ?

  • A βƒ–       βƒ— 𝑇 π‘Š
  • B βƒ–     βƒ— 𝑇 𝑋
  • C βƒ–     βƒ— 𝑋 𝑍
  • D βƒ–       βƒ— 𝑉 π‘Š
  • E βƒ–     βƒ— 𝑉 𝑍

Q8:

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

  • A βƒ–       βƒ— π‘Š 𝑋
  • B βƒ–       βƒ— 𝑉 π‘Š
  • C βƒ–       βƒ— π‘Š π‘Œ
  • D βƒ–     βƒ— 𝑇 𝑋
  • E βƒ–     βƒ— π‘Œ 𝑍

Q9:

Name the following figure.

  • A line segment 𝐻 𝐾
  • B line βƒ–    βƒ— 𝐽 𝐾
  • C ray οƒͺ 𝐻 𝐽
  • D plane 𝐻 𝐽 𝐾
  • E line βƒ–      βƒ— 𝐻 𝐾

Q10:

How many planes are in the figure?

Q11:

How many planes appear in the figure?

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:

Complete: If βƒ– βƒ— 𝐿 is parallel to the plane 𝑋 , then βƒ– βƒ— 𝐿 ∩ 𝑋 = .

  • A 𝑋
  • B βƒ– βƒ— 𝐿
  • C βˆ…

Q14:

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.

Q15:

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

  • A βƒ–       βƒ— 𝑇 π‘Š
  • B βƒ–     βƒ— 𝑇 π‘Œ
  • C βƒ–     βƒ— π‘Œ 𝑍
  • D βƒ–       βƒ— 𝑋 π‘Š
  • E βƒ–       βƒ— π‘Š 𝑍

Q16:

What is 𝑀 𝐢 ∩ 𝐴 𝐡 ?

  • A { 𝐢 }
  • B { 𝑀 }
  • C { 𝐡 }
  • D βˆ…

Q17:

Describe what is shown in the figure.

  • AA plane 𝐴 𝐡 𝐢 intersected by 𝐢 𝐡
  • BA plane 𝐡 𝐢 𝐷 intersected by 𝐴 𝐸
  • CA plane 𝐴 𝐡 𝐢 intersected by 𝐷 𝐸

Q18:

The given figure shows a pentagonal prism placed on a plane 𝐴 , find the intersection of plane 𝐴 and the plane 𝑆 𝑇 𝑃 .

  • Apoint 𝑇
  • Bpoint 𝑆
  • C βƒ–    βƒ— 𝑆 𝑃
  • D βƒ–    βƒ— 𝑆 𝑇
  • E βƒ–     βƒ— 𝑇 𝑃

Q19:

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

  • A
  • B
  • C

Q20:

Which of the following is a line containing the point π‘Š ?

  • A βƒ–       βƒ— 𝑇 π‘Š
  • B βƒ–     βƒ— 𝑇 π‘Œ
  • C βƒ–     βƒ— π‘Œ 𝑍
  • D βƒ–      βƒ— 𝑉 π‘Œ
  • E βƒ–     βƒ— 𝑉 𝑍

Q21:

Which of the following holds?

  • A 𝐿 ∈ 𝑋
  • B 𝐿 βŠ„ 𝑋
  • C 𝐿 βˆ‰ 𝑋
  • D 𝐿 βŠ‚ 𝑋

Q22:

Which of the following lines contains the point 𝑉 ?

  • A βƒ–       βƒ— 𝑇 π‘Š
  • B βƒ–     βƒ— 𝑇 π‘Œ
  • C βƒ–     βƒ— π‘Œ 𝑍
  • D βƒ–       βƒ— 𝑋 π‘Š
  • E βƒ–     βƒ— 𝑋 𝑍

Q23:

How many planes can pass through one given point?

  • A1
  • B2
  • C0
  • Dan infinite number