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Lesson 7 of 15

Diagonals that cut each other in half

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7 min

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Draw a parallelogram. Join each corner to the corner opposite it. These two lines are the diagonals. Where do they cross?

A parallelogram, both diagonals drawn, crossing at O.
Step 1 of 4
  1. A parallelogram, both diagonals drawn, crossing at O.
  2. One diagonal splits into two pieces: 4 and 4.
  3. The other splits into two pieces: 3 and 3.
  4. Each diagonal is cut exactly in half.

They cross at the middle of each diagonal. A parallelogram's diagonals halve each other.

Rule: A parallelogram's two diagonals bisect each other. Each diagonal is cut into two equal halves at the crossing point.

Halving does not make the two diagonals equal. One diagonal is 4 + 4 = 8 long. The other is 3 + 3 = 6 long. Halving and equal length are two separate facts.

A shape with exactly one parallel pair does not halve its diagonals.

Drag a corner. Watch the pieces of each diagonal. Switch the toggle off, and one corner moves alone.

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