Pythagorean Theorem

What you’ll learn

• In a right triangle with legs $a$, $b$ and hypotenuse $c$, the Pythagorean Theorem states $a^2+b^2=c^2$.
• The converse checks whether a triangle is right by testing whether the longest side satisfies the same relationship with the two shorter sides.
• Modeling problems (ladders, rectangles, diagonals) need a clear sketch so you know which segments are legs and which play the role of $c$.
• Common errors include adding side lengths instead of squaring them, or mis-labeling the hypotenuse when applying the converse.