Pythagorean Theorem in Three Dimensions

Start with the reference sheet and the hypotenuse and leg drills, then move to mixed practice and word problems. Use the proof and converse sheets to deepen understanding, and the code breaker for review.

Find box diagonals in two steps through the bottom face, plus a cone's slant height from d = 14 cm. The directions on the page read: Find each x in two steps and show both. For a box, first find y, the bottom face diagonal. For the cone, first find the radius. Round x to the nearest tenth if needed. An answer key is included.

Yes, both. We made it for 8th grade Pythagorean theorem, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.

Square both legs, add them and take the square root. With legs of 12 ft and 5 ft, 144 + 25 = 169, so the hypotenuse is 13 ft. Pythagorean Theorem, Find the Hypotenuse has eight triangles.

It is a set of three whole numbers that fit a² + b² = c², such as 8, 15, 17. Multiples of a triple, like 9, 12, 15, are triples too. Pythagorean Triples, Spot and Scale Them asks students to test twelve sets.

One proof places four copies of a right triangle inside a square with side a + b in two ways. Setting the two area expressions equal leaves a² + b² = c². Prove the Pythagorean Theorem With Square Areas guides each step.

Find the diagonal of the bottom face first, then use it as a leg with the height to find the space diagonal. Pythagorean Theorem in Three Dimensions practices this with boxes and a cone.