Lesson Worksheet: Points, Lines, and Planes in Space Mathematics • 11th Grade

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

Q1:

Find the straight lines that pass through the point 𝐡.

  • A⃖⃗𝐡𝑀,⃖⃗𝐷𝑀,⃖⃗𝐷𝐢
  • B⃖⃗𝐡𝐴,⃖⃗𝐴𝑀,⃖⃗𝑀𝐡
  • C⃖⃗𝐡𝐴,⃖⃗𝐡𝑀,⃖⃗𝐡𝐢
  • D⃖⃗𝐡𝑀,⃖⃗𝐡𝐢,⃖⃗𝐢𝑀

Q2:

Consider the cuboid 𝐴𝐡𝐢𝐷𝐸𝐹𝐺𝐻, where 𝐴𝐡≠𝐡𝐢≠𝐴𝐸.

What can be said about 𝐸𝐹 and 𝐹𝐺?

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

What can be said about 𝐴𝐸 and 𝐢𝐺?

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

What can be said about 𝐡𝐷 and 𝐷𝐻?

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

What can be said about 𝐡𝐷 and 𝐴𝐢?

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

Q3:

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

  • A𝐷𝐢
  • B𝐢𝐡
  • C𝐻𝐺
  • D𝐹𝐡
  • E𝐸𝐻

Q4:

Find three planes that pass through both of the points 𝐴 and 𝐡.

  • A𝐴𝐡𝐢, 𝐴𝐡𝐡′, 𝐴𝐡𝐢′
  • B𝐴𝐡𝐢, 𝐷𝐢𝐢′, 𝐢′𝐷′𝐴′
  • C𝐴𝐡𝐡′, 𝐴𝐡𝐢, 𝐴𝐷𝐷′
  • D𝐴𝐡𝐡′, 𝐴𝐡𝐢, 𝐡𝐢𝐢′

Q5:

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.

Q6:

Complete: If ⃖⃗𝐿 is parallel to the plane 𝑋, then βƒ–βƒ—πΏβˆ©π‘‹=.

  • A𝑋
  • B⃖⃗𝐿
  • Cβˆ…

Q7:

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

  • A
  • B
  • C

Q8:

What is the intersection of the plane through 𝐴𝐡𝐡′𝐴′ and the plane through 𝐡𝐢𝐢′𝐡′?

  • A⃖⃗𝐡𝐡′
  • Bβˆ…
  • C⃖⃗𝐴𝐡
  • D⃖⃗𝐴′𝐡′

Q9:

What is the intersection of planes 𝑀𝐴𝐡, 𝑀𝐡𝐢, and 𝑀𝐴𝐢?

  • Aβˆ…
  • B𝑀𝐡
  • C{𝑀}
  • D{𝐡}

Q10:

Consider the following figure.

Write another name for the plane 𝒫.

  • APlane 𝐷𝐸𝐹
  • BPlane 𝐴𝐡𝐸𝐷
  • CPlane 𝐴𝐡𝐢
  • DPlane 𝐴𝐢𝐹𝐷
  • EPlane 𝐡𝐢𝐹𝐸

How many planes are shown in the figure?

Which two planes intersect in 𝐴𝐷?

  • APlane 𝐴𝐢𝐹𝐷 and plane 𝐴𝐡𝐸𝐷
  • BPlane 𝐴𝐢𝐹𝐷 and plane 𝐴𝐡𝐢
  • CPlane 𝐴𝐢𝐹𝐷 and plane 𝐷𝐸𝐹
  • DPlane 𝐴𝐡𝐸𝐷 and plane 𝐷𝐸𝐹
  • EPlane 𝐴𝐡𝐢 and plane 𝐴𝐡𝐸𝐷

Are planes 𝒫 and 𝐷𝐸𝐹 parallel or intersecting?

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

This lesson includes 90 additional questions and 9 additional question variations for subscribers.

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