Geometry – The Pythagorean Theorem

In this lesson we will lean how to identify and using the Pythagorean Theorem when working with right triangles and identify common Pythagorean triples:

1. Pythagorean theorem: How the sides of right triangles are related
2. Pythagorean triples: When whole numbers are the sides of right triangles
3. Generating triples: Ways to write out every last Pythagorean triple
4. Distance formula: Find the distance between any two points
5. Equilateral area: Finding the area of equilateral and isosceles triangles
6. Heron's formula: Another way to find the area of a triangle
7. Proving Heron's formula: You might know the formula, but where does it come from?

The Pythagorean Theorem given a right triangle with length legs a and b and c as hypotenuse of length by a2 + b2 = c2
Three whole numbers that are side lengths of a right triangle called Pythagorean triple.
Right triangle Pythagorean Theorem a2 + b2 = c2
How to use the Pythagorean Theorem to derive the distance formula
You have already learned how to use Pythagorean Theorem to understand different types of right triangles, find missing lengths, and we can also apply the Pythagorean Theorem to a coordinate grid and find distances between points.
Equilateral triangle all sides have the same length, all angles have the same measure and each angle measure exactly 60 degrees.
Isosceles triangle has at least two congruent sides that are called the legs of the triangle, the other side is called the base, and the angle made by the two legs of the isosceles triangle is called the vertex angle.

Geometry – The Pythagorean Theorem | Pythagorean triples: 

Geometry – The Pythagorean Theorem - Generating triples | Distance formula: 

Geometry – The Pythagorean Theorem - Equilateral Area | Heron's Formula: 

Geometry – The Pythagorean Theorem - Proving Heron's formula: