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Worksheet: Pythagoras' Theorem in 3D

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

Q1:

𝐴 𝐡 𝐢 𝐷 𝐴 β€² 𝐡 β€² 𝐢 β€² 𝐷 β€² is a cube. Determine the lengths 𝐴 β€² 𝐡 and 𝐴 𝐢 .

  • A 𝐴 β€² 𝐡 = 9 7 , 𝐴 𝐢 = 9 7 √ 2
  • B 𝐴 β€² 𝐡 = 9 7 √ 2 , 𝐴 𝐢 = 9 7
  • C 𝐴 β€² 𝐡 = 9 7 , 𝐴 𝐢 = 9 7
  • D 𝐴 β€² 𝐡 = 9 7 √ 2 , 𝐴 𝐢 = 9 7 √ 2

Q2:

𝐴 𝐡 𝐢 𝐷 𝐴 β€² 𝐡 β€² 𝐢 β€² 𝐷 β€² is a cube. Determine the lengths 𝐴 β€² 𝐡 and 𝐴 𝐢 .

  • A 𝐴 β€² 𝐡 = 9 3 , 𝐴 𝐢 = 9 3 √ 2
  • B 𝐴 β€² 𝐡 = 9 3 √ 2 , 𝐴 𝐢 = 9 3
  • C 𝐴 β€² 𝐡 = 9 3 , 𝐴 𝐢 = 9 3
  • D 𝐴 β€² 𝐡 = 9 3 √ 2 , 𝐴 𝐢 = 9 3 √ 2

Q3:

𝐴 𝐡 𝐢 𝐷 𝐴 β€² 𝐡 β€² 𝐢 β€² 𝐷 β€² is a cube. Determine the lengths 𝐴 β€² 𝐡 and 𝐴 𝐢 .

  • A 𝐴 β€² 𝐡 = 5 6 , 𝐴 𝐢 = 5 6 √ 2
  • B 𝐴 β€² 𝐡 = 5 6 √ 2 , 𝐴 𝐢 = 5 6
  • C 𝐴 β€² 𝐡 = 5 6 , 𝐴 𝐢 = 5 6
  • D 𝐴 β€² 𝐡 = 5 6 √ 2 , 𝐴 𝐢 = 5 6 √ 2

Q4:

𝐴 𝐡 𝐢 𝐷 𝐴 β€² 𝐡 β€² 𝐢 β€² 𝐷 β€² is a cube. Determine the lengths 𝐴 β€² 𝐡 and 𝐴 𝐢 .

  • A 𝐴 β€² 𝐡 = 5 , 𝐴 𝐢 = 5 √ 2
  • B 𝐴 β€² 𝐡 = 5 √ 2 , 𝐴 𝐢 = 5
  • C 𝐴 β€² 𝐡 = 5 , 𝐴 𝐢 = 5
  • D 𝐴 β€² 𝐡 = 5 √ 2 , 𝐴 𝐢 = 5 √ 2

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