Squares on a Right Triangle

A right triangle has a square built on each of its three sides. The two smaller squares together cover exactly as much area as the biggest one.

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In the picture

The brass angle marker lying in the triangle’s square corner, where the two short sides meet.
The small teal square, built on the shortest side of the triangle.
The mustard square, built on the other short side, the one that meets the teal square at the square corner.
The large coral square, built on the longest side, across from the square corner.

Examples

A ladder leaning on a wall: the height on the wall and the distance of its feet from the wall give the ladder’s length.
Walking 3 blocks east and then 4 blocks north leaves you exactly 5 blocks from where you started.

Key takeaways

The rule works only when the triangle has a square corner (a right angle).
Area of the small square + area of the medium square = area of the largest square (a² + b² = c²).