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Quadrilaterals

A rectangle also has matching diagonals

A carpenter checks a door frame with a tape, corner to corner. Why does that work?

A rectangle, 8 by 6. Both diagonals measure 10.
Step 1 of 4
  1. A rectangle, 8 by 6. Both diagonals measure 10.
  2. Lean the top. The sides stay 8 and 6. The corners are no longer 90°.
  3. The diagonals are now about 12.2 and 7.2.
  4. Equal diagonals happen only at a right angle.

Equal readings show a rectangle, if both pairs of sides are parallel.

Rule: A parallelogram whose diagonals are equal is a rectangle. That is the carpenter's check. A door frame has parallel opposite sides. So it is a parallelogram. Equal tape readings then show all four corners are square.

Equal diagonals alone are not enough. A shape has a bottom of 8 and a height of 6. Its top is 2 long and sits in the middle. The top is 3 in from each end. Its diagonals are both about 7.8. Only one pair of its sides is parallel. So it is not a parallelogram.

Drag the slider to lean the frame. Find where the diagonals match.

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This track

  1. 0 Start here
  2. 1 Four straight sides, joined up
  3. 2 The four angles come to 360°
  4. 3 A line to the corner across
  5. 4 Five names and what each one demands
  6. 5 What a parallelogram gives you
  7. 6 Checkpoint: sides, angles and the family
  8. 7 Diagonals that cut each other in half
  9. 8 A rectangle also has matching diagonals
  10. 9 A rhombus crosses at a right angle
  11. 10 One shape, several names
  12. 11 Building one from measurements
  13. 12 Checkpoint: diagonals, names and building
  14. 13 The big picture
  15. 14 Track quiz

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