The Pythagorean Theorem
The Pythagorean theorem is ancient and indispensable. Students discover that in a right triangle, the squares on the two legs add to the square on the hypotenuse — and learn to apply it in both directions (finding a missing side; checking whether a triangle is right-angled). Distance problems on coordinate grids give the theorem immediate geometric meaning.
What students explore
The Pythagorean theorem is ancient and indispensable. Students discover that in a right triangle, the squares on the two legs add to the square on the hypotenuse — and learn to apply it in both directions (finding a missing side; checking whether a triangle is right-angled). Distance problems on coordinate grids give the theorem immediate geometric meaning.
Key ideas
State and apply the Pythagorean theorem: a² + b² = c². Determine whether a triangle is a right triangle using the converse. Find missing side lengths in right triangles. Apply the theorem to real-world distance and measurement problems.
Putting it together
Apply these ideas through worked examples, guided practice, and real-world problems.