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Pythagorean Theorem
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What you will learn from this videoWhat you will learn
- We'll learn about the Pythagorean Theorem.
- That we can use the Pythagorean Theorem to find the lengths of all sides in a right triangle.
- We'll see that this knowledge can help us make a skateboard ramp, build a home for bees and even watch a movie!
- Discussion Questions
Before Video
What different kinds of triangles are there?ANSWERScalene, isosceles, equilateral, acute, right, obtuse.
Yes, the base and height can be congruent.
No, if all three sides were the same length, the triangle would only have 60° angles.
Base, height, and hypotenuse (it’s okay if students don’t name the “hypotenuse” yet).
It depends on your point of view. The base is generally the bottom and the height is at a right angle to it, but the triangle can be rotated so that the side names are swapped.
After Video
When can you use the Pythagorean Theorem?ANSWERWhen I know two side lengths in a right triangle, and I want to calculate the missing side length.
a^{2}=a⋅a, whereas 2a=a+a. For example, 3^{2}=9 and 3×2=6.
Substitute these values into the Pythagorean Theorem to get 6^{2}+8^{2}=c^{2}. Simplify to 100=c^{2}, and then take the square root to get 10 units.
I can still substitute 6 for a, but now I substitute 8 for c instead of b. The formula 6^{2}+b^{2}=8^{2} yields 36+b^{2}=64, or b^{2}=28. The exact value is square root of 28, which is about 5.3 units, rounded to the nearest tenth.
I draw a triangle with the hypotenuse along the diagonal line that I want to measure. I count the lengths of the legs and substitute them for a and b in the Pythagorean Theorem. Then I can solve for c to find its length.
- Vocabulary
- Legs DEFINE
The shorter two sides of a right triangle, often denoted by a and b.
- Hypotenuse DEFINE
The longest side of a right triangle, often denoted by c.
- Pythagorean Theorem DEFINE
In a right triangle, the square of the longest side is equal to the sum of the squares of the shorter two sides. This is represented by the formula a^{2} + b^{2}= c^{2}.
- Square root DEFINE
A value that, when multiplied by itself, gives the number.
- Irrational number DEFINE
A number whose decimal places go on forever with no pattern.
- Converse of the Pythagorean Theorem DEFINE
If three lengths make the formula a^{2} + b^{2}= c^{2} true, then the three lengths can form a right triangle.
- Legs DEFINE
- Reading Material
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
- Teacher Guide