How it works
This Pythagorean theorem graphic organizer starts with the student's own drawing. Once the hypotenuse is labeled c, it is plain whether a problem asks to add the squares or to subtract them.
Read the full guide
Label the hypotenuse first
The hypotenuse is the side opposite the right angle, and it is always the longest side. Have students find the right angle and mark the side across from it as c before any number goes into the rule. The legs can be a and b in either order.
Test a triangle with the rule
The rule also runs backward. If the squares of the two shorter sides add up to the square of the longest side, the triangle has a right angle. If they do not, it has none.
- A length is never negative, so keep only the positive square root.
- 3, 4, 5 makes a right triangle, and so does any multiple of it, such as 6, 8, 10.
Questions and answers
What is the Pythagorean theorem in simple terms?
In a right triangle, square the two shorter sides and add them: the total is the square of the longest side. With legs a and b and hypotenuse c, that is written a² + b² = c².
How do you find the hypotenuse of a right triangle?
Square each leg, add the two squares, then take the square root of the sum. With legs 3 and 4: 9 + 16 = 25, and the square root of 25 is 5.
How do you find a missing leg with the Pythagorean theorem?
Square the hypotenuse and the leg you know, subtract the smaller square from the larger, then take the square root. With hypotenuse 13 and leg 5: 169 − 25 = 144, so the other leg is 12.
What grade is the Pythagorean theorem taught?
In the Common Core standards it is 8th grade work. Students explain a proof of the theorem and its converse, find unknown side lengths in right triangles, and find the distance between two points in a coordinate system.