Pythagorean Theorem

Contributor: Mason Smith. Lesson ID: 11075

If there is a right triangle, is there such a thing as a wrong triangle? Maybe not, but there is a right way to measure any side of a right triangle using the Pythagorean Theorem! Easy to learn, too!


Geometry, Plane Geometry (2D)

learning style
personality style
Grade Level
Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!

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  • How can a right triangle make the world more measurable?
  • How can we use one of the simplest shapes to solve infinite problems in our daily lives?

Take a look at this map:

path around the lake

Sammy has walked from Mrs. White's house to the Supermarket and back — with groceries — every day for the whole school year, but afterwards, her legs are absolutely exhausted!

  • What would be a faster and straighter way for Sammy to bring groceries to Mrs. White's house?

Measure how far Sammy would have to go in order to go around the Lake.

  • What if she could build a bridge straight across the lake to the Supermarket instead of going around?
  • How long would that bridge have to be?

Is there an easier way to figure out the exact distance if Sammy knows she must go 3000 feet down one side of the lake and then, after turning the corner, she must travel another 4000 feet?

Take a moment to try to solve this problem:

  • How can I get an answer of 5000 feet using two pluses, two multiplication signs, two square roots, and an equal sign?

Click on the 3-4-5-Triangle from Math is Fun for some hints if you are stuck!

Now that you know we must solve 30002 + 40002 = c2, we can use the Pythagorean Theorem to solve all sorts of problems! All we need to know is:

  • The two shortest sides next to the right angle are called the "legs."
  • The hypotenuse is the longest side, that is across the triangle from the right angle.
  • If we take the sum of the legs squared ("squared" means "times themselves"), then we can get the hypotenuse squared.
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