Lesson Worksheet: Three-Dimensional Figures Mathematics

In this worksheet, we will practice identifying 3D shapes and their properties.

Q1:

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.

Q2:

Which of the following is the plan of the given shape?

  • A
  • B
  • C
  • D
  • E

Q3:

Find the straight lines that pass through the point 𝐵.

  • A𝐵𝑀,𝐷𝑀,𝐷𝐶
  • B𝐵𝐴,𝐴𝑀,𝑀𝐵
  • C𝐵𝐴,𝐵𝑀,𝐵𝐶
  • D𝐵𝑀,𝐵𝐶,𝐶𝑀

Q4:

Consider the cuboid 𝐴𝐵𝐶𝐷𝐸𝐹𝐺𝐻, where 𝐴𝐵𝐵𝐶𝐴𝐸.

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 𝐶𝐺?

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

What can be said about 𝐵𝐷 and 𝐷𝐻?

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

What can be said about 𝐵𝐷 and 𝐴𝐶?

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

Q5:

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

  • A𝐷𝐶
  • B𝐶𝐵
  • C𝐻𝐺
  • D𝐹𝐵
  • E𝐸𝐻

Q6:

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

  • A
  • B𝑀𝐵
  • C{𝑀}
  • D{𝐵}

Q7:

How many vertices does a rectangular prism have?

Q8:

How many faces does a rectangular prism have?

Q9:

How many edges does a rectangular prism have?

Q10:

Consider the following figure.

How many edges does this shape have?

How many vertices does it have?

How many faces does it have?

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