Two pages of visual notes for students to keep: the key words with pictures, the squares-on-the-sides picture that shows why the theorem works, four solved problems in the style of the Pythagorean Platforms game, and where right triangles show up in real life. To make a PDF, click Print and choose "Save as PDF."
Visual Notes: The Pythagorean Theorem
Grade 8 · CCSS 8.G.B.6, 8.G.B.7 · Pairs with the Pythagorean Platforms game
Name
The big idea: in any right triangle, the squares on the two short sides together have the same area as the square on the long side: a² + b² = c². In the picture, 9 + 16 = 25. Know two sides and you can always find the third.
Key vocabulary
Right triangle
A triangle with one right angle (90°), marked with a little box.
Legs (a and b)
The two sides that make the right angle.
Hypotenuse (c)
The longest side, across from the right angle.
Pythagorean theorem
a² + b² = c²
True for every right triangle, and only for right triangles.
Square root (√)
The number that times itself gives the original: √25 = 5, because 5 × 5 = 25.
A TV screen is 40 in wide and 30 in tall. TVs are sold by the diagonal.
The width, height and diagonal make a right triangle.
30² + 40² = 900 + 1600 = 2500
Diagonal = √2500 = 50 in: a “50-inch TV”
✓ Check: it's the 3-4-5 triangle, times 10
4. Is it a right triangle?
Sides 9, 12 and 15.
The longest side would be c: c = 15.
9² + 12² = 81 + 144 = 225
15² = 225. They match, so yes, it's a right triangle.
✓ If they don't match (like 6, 7, 9: 36 + 49 = 85, not 81), it isn't.
Watch out
Square the sides before adding: 6 + 8 = 14 is wrong; 6² + 8² = 100, so c = 10.
4² means 4 × 4 = 16, not 4 × 2.
The hypotenuse goes by itself on one side of the equation. Finding a leg means subtracting.
Where you see it in real life
Ladders: the ladder is the hypotenuse.TVs: the size is the diagonal.Baseball: the throw from home to second cuts across the square.Ramps: the slope is the hypotenuse.