Pythagorean Theorem

Section 1The rule

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This is written as a^2 + b^2 = c^2, where c is the hypotenuse.

Section 2Finding the hypotenuse

If the two shorter sides are known, square both, add them, then take the square root. For example, sides 6 cm and 8 cm give c^2 = 36 + 64 = 100, so c = 10 cm.

Section 3Finding a shorter side

If the hypotenuse and one shorter side are known, subtract the square of the known shorter side from the square of the hypotenuse, then take the square root.

Section 4Checking right triangles

The theorem only works for right-angled triangles. Look for the square corner mark or information that says the angle is 90 degrees.

Section 5Real-life uses

Pythagoras can find diagonal distances, ladder lengths, heights, and distances across rectangles. Always write the units in the final answer.