The Pythagorean Theorem: Practice at Home, Grade 8

The Pythagorean theorem links the three sides of a right triangle. In Grade 8, children use it to find a missing side, and it turns up in building, maps and screens.

What your child is working on

In a right triangle, the two shorter sides (a and b) and the longest side, the hypotenuse (c), follow a² + b² = c². For sides 3 and 4: 9 + 16 = 25, so c = 5. Another example: 5 and 12 give 25 + 144 = 169, so c = 13.

Try it at home

Check it with a real corner. Measure 3 feet along one wall at the floor and 4 feet along another, from the corner. The straight line between those two marks should be 5 feet if the corner is a true right angle. This is a trick builders use.

Then try a ladder problem: a 10-foot ladder leans against a wall with its foot 6 feet from the wall. How high does it reach? 10² − 6² = 100 − 36 = 64, so 8 feet.

Where children slip

Adding when the unknown is a short side. If c is known, subtract: a² = c² − b². Also forgetting the final square root.

Practice online

The free Find the hypotenuse of a right triangle page starts with the hypotenuse, as in the 3-4-5 example, and gives short sets. All Grade 8 skills are listed by topic.