Same Math › Grade 8 › The Pythagorean theorem with squares
How is the Pythagorean theorem taught now?
In a right triangle, the squares built on the two shorter sides add up to the square on the longest side: a² + b² = c². With legs 3 and 4, the squares are 9 and 16, which make 25, so the longest side is 5. Classes show the squares before the formula.
- Legs a and b: the two sides that meet at the right angle.
- Hypotenuse c: the longest side, across from the right angle.
- a² + b² = c²: areas, not just numbers.
Why schools teach it
Kids should know why, not just the formula
Eighth graders explain a proof of the theorem (8.G.B.6) and use it to find missing sides in real and math problems (8.G.B.7). Seeing the squares as areas helps kids remember which side is c and why the numbers get squared.
Teachers often use cut-out squares or grid paper so kids can check that the areas really add up.
At the kitchen table
What to say, and what to skip
Say this
Which side is across from the right angle?
That's c.What's the area of the square on each leg?
Do the two small areas add up to the big one?
Is your answer longer than both legs?
c must be the longest side.
Skip this
a + b = c.
The lengths don't add; the squares do.- Plugging the hypotenuse in as a or b.c is always the side across from the right angle.
- Forgetting the square root at the end.c² = 25 means c = 5, not 25.
See it in action
Finding a missing leg
The hypotenuse is 13 and one leg is 5
5² + b² = 13²Work out the squares and subtract
b² = 169 − 25 = 144Take the square root
b = 12
Sets like 3-4-5, 5-12-13 and 8-15-17 give whole-number answers. Classes use them a lot.
Free practice sheet
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Parents also ask
Does it work for every triangle?
Only right triangles, with one 90° angle.
What's a Pythagorean triple?
Three whole numbers that fit, like 3, 4, 5 or 5, 12, 13.
What if the answer isn't a whole number?
Leave it as a square root, like √20, or round as the problem asks.
Where is this used?
Measuring diagonals, like a TV screen or a shortcut across a park.