Worksheet: Pythagoras' Theorem in 3D

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In this worksheet, we will practice using Pythagoras's theorem in three dimensions to solve geometry problems in three dimensions.

Q1:

𝐴 𝐵 𝐶 𝐷 𝐴 ′ 𝐵 ′ 𝐶 ′ 𝐷 ′ is a cube. Determine the lengths 𝐴 ′ 𝐵 and 𝐴 𝐶 .

  • A 𝐴 ′ 𝐵 = 9 7 , 𝐴 𝐶 = 9 7 √ 2
  • B 𝐴 ′ 𝐵 = 9 7 √ 2 , 𝐴 𝐶 = 9 7
  • C 𝐴 ′ 𝐵 = 9 7 , 𝐴 𝐶 = 9 7
  • D 𝐴 ′ 𝐵 = 9 7 √ 2 , 𝐴 𝐶 = 9 7 √ 2

Q2:

𝐴 𝐵 𝐶 𝐷 𝐴 ′ 𝐵 ′ 𝐶 ′ 𝐷 ′ is a cube. Determine the lengths 𝐴 ′ 𝐵 and 𝐴 𝐶 .

  • A 𝐴 ′ 𝐵 = 9 3 , 𝐴 𝐶 = 9 3 √ 2
  • B 𝐴 ′ 𝐵 = 9 3 √ 2 , 𝐴 𝐶 = 9 3
  • C 𝐴 ′ 𝐵 = 9 3 , 𝐴 𝐶 = 9 3
  • D 𝐴 ′ 𝐵 = 9 3 √ 2 , 𝐴 𝐶 = 9 3 √ 2

Q3:

𝐴 𝐵 𝐶 𝐷 𝐴 ′ 𝐵 ′ 𝐶 ′ 𝐷 ′ is a cube. Determine the lengths 𝐴 ′ 𝐵 and 𝐴 𝐶 .

  • A 𝐴 ′ 𝐵 = 5 6 , 𝐴 𝐶 = 5 6 √ 2
  • B 𝐴 ′ 𝐵 = 5 6 √ 2 , 𝐴 𝐶 = 5 6
  • C 𝐴 ′ 𝐵 = 5 6 , 𝐴 𝐶 = 5 6
  • D 𝐴 ′ 𝐵 = 5 6 √ 2 , 𝐴 𝐶 = 5 6 √ 2

Q4:

𝐴 𝐵 𝐶 𝐷 𝐴 ′ 𝐵 ′ 𝐶 ′ 𝐷 ′ is a cube. Determine the lengths 𝐴 ′ 𝐵 and 𝐴 𝐶 .

  • A 𝐴 ′ 𝐵 = 5 , 𝐴 𝐶 = 5 √ 2
  • B 𝐴 ′ 𝐵 = 5 √ 2 , 𝐴 𝐶 = 5
  • C 𝐴 ′ 𝐵 = 5 , 𝐴 𝐶 = 5
  • D 𝐴 ′ 𝐵 = 5 √ 2 , 𝐴 𝐶 = 5 √ 2

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