3D Pythagoras (Edexcel GCSE Maths): Flashcards

Extension of 2D Pythagoras to three dimensions

Longest line through 3D shape interior, corner to opposite corner

$a^2 + b^2 + c^2 = d^2$

Three perpendicular edges of the cuboid

Space diagonal from corner to opposite corner

2D Pythagoras applied twice in succession

Find base diagonal: $e^2 = a^2 + b^2$

Use diagonal & height: $d^2 = e^2 + c^2$

All dimensions equal, only need one measurement

Can be adapted to solve problems with pyramids and other 3D shapes

Identify the shape

Find the three perpendicular dimensions