a² + b² = c², used forward for the hypotenuse, backward for a leg, and once more on the grid.
The answer key prints on a separate page.
The theorem is one equation used two ways, and separating them is the point of the first two sections. Finding the hypotenuse is the equation forward — square the two legs, add, take the root. Finding a leg is the same equation rearranged, and the reliable error is running it forward anyway: adding when the missing side is a leg gives an answer larger than the hypotenuse, which is impossible and worth teaching a child to notice.
The distance section is included because the distance formula is not a new rule — it is Pythagoras laid over a coordinate grid, with the horizontal and vertical gaps as the two legs. A child who has the theorem but freezes at two points has not met new mathematics; they have not yet seen that the grid draws the right triangle for them.
