What different kinds of triangles are there?

Scalene, isosceles, equilateral, acute, right, obtuse.

In a right triangle, can two sides be the same length?

Yes, the base and height can be congruent.

In a right triangle, can three sides be the same length?

No, if all three sides were the same length, the triangle would only have 60° angles.

What are the sides of a right triangle called?

Base, height, and hypotenuse (it’s okay if students don’t name the “hypotenuse” yet).

Which side of a triangle is the base and which side is the height?

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.

When can you use the Pythagorean Theorem?

When I know two side lengths in a right triangle, and I want to calculate the missing side length.

How is squaring, as in a<sup>2</sup>, different from doubling, as in 2a?

a2=a⋅a, whereas 2a=a+a. For example, 32=9 and 3×2=6.

How would you find the length of the longest side of a triangle if the shorter two sides measure 6 units and 8 units?

Substitute these values into the Pythagorean Theorem to get 62+82=c2. Simplify to 100=c2, and then take the square root to get 10 units.

How would your calculations change if one leg measures 6 units and the hypotenuse measures 8 units?

I can still substitute 6 for a, but now I substitute 8 for c instead of b. The formula 62+b2=82 yields 36+b2=64, or b2=28. The exact value is square root of 28, which is about 5.3 units, rounded to the nearest tenth.

How can the Pythagorean Theorem help you find a distance on the coordinate plane?

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.

Pythagorean Theorem

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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?ANSWER
  - Scalene, isosceles, equilateral, acute, right, obtuse.
  In a right triangle, can two sides be the same length?ANSWER
  - Yes, the base and height can be congruent.
  In a right triangle, can three sides be the same length?ANSWER
  - No, if all three sides were the same length, the triangle would only have 60° angles.
  What are the sides of a right triangle called?ANSWER
  - Base, height, and hypotenuse (it’s okay if students don’t name the “hypotenuse” yet).
  Which side of a triangle is the base and which side is the height?ANSWER
  - 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?ANSWER
  - When I know two side lengths in a right triangle, and I want to calculate the missing side length.
  How is squaring, as in a², different from doubling, as in 2a?ANSWER
  - a²=a⋅a, whereas 2a=a+a. For example, 3²=9 and 3×2=6.
  How would you find the length of the longest side of a triangle if the shorter two sides measure 6 units and 8 units?ANSWER
  - Substitute these values into the Pythagorean Theorem to get 6²+8²=c². Simplify to 100=c², and then take the square root to get 10 units.
  How would your calculations change if one leg measures 6 units and the hypotenuse measures 8 units?ANSWER
  - I can still substitute 6 for a, but now I substitute 8 for c instead of b. The formula 6²+b²=8² yields 36+b²=64, or b²=28. The exact value is square root of 28, which is about 5.3 units, rounded to the nearest tenth.
  How can the Pythagorean Theorem help you find a distance on the coordinate plane?ANSWER
  - 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
- Hypotenuse DEFINE
- Pythagorean Theorem DEFINE
- Square root DEFINE
- Irrational number DEFINE
- Converse of the Pythagorean Theorem DEFINE
Reading Material
Practice Word Problems
Practice Number Problems
Lesson Plan
Teacher Guide
Assessment
Online Quiz Game Quiz PDF Exit Ticket