Pythagorean Theorem – NFL and Geometry ⋆ GeometryCoach.com

Pythagorean Theorem and its Converse Guided Notes

A Right-Angled Triangle (named as right triangle) is a triangle which has one of its angles equal to 90 degrees.

There are properties associated with a right triangle.

• A Hypotenuse is the line segment opposite to the right-angle. The Hypotenuse is also the longest side of a Right Triangle.
• An Opposite is the line segment opposite to the angle ϴ.
• An Adjacent is the line segment next to the angle ϴ.
• The sum of three angles is 180°
  e. ϴ + φ + 90° = 180°

Pythagorean Theorem

In a Right Triangle, the sum of the squares of the lengths of adjacent and opposite side is equal to the square of the length of hypotenuse.

a²+b²=c²

Where,

c= Hypotenuse

a= Opposite

b= Adjacent

Problem 1: Find the unknown length in the right triangle shown.

By Pythagorean theorem,

c²=a²+b²

This means that,

13²=x²+12²

x²=169-144

x²=25

x=5

Converse of Pythagorean Theorem

If the sum of the squares of the lengths of adjacent and opposite sides is equal to the square of the length of hypotenuse, then the triangle is a right triangle.

Where,

c= Hypotenuse

a= Opposite

b= Adjacent

Problem 2: Identify if the triangle shown is a right triangle or not.

To show if the triangle is a right triangle, we need to check whether its lengths satisfy the Pythagorean theorem:

c²=a²+b²

If this triangle is right then this also must be true,

10²=8²+6²

100=64+36

100=100

So, the triangle is a right triangle.

Another Super Engaging Pythagorean Theorem Lesson:

If you are still struggling to get your students engaged with your Pythagorean Theorem Lesson we have another lesson available on PreAlgebraCoach.com. The lesson teaches the students to derive the Pythagorean Theorem on their own rather than just giving it to them and then some sample problems. The lesson below is an extremely engaging way to teach the Pythagorean Theorem and its Converse. I would recommend teaching it this way then go through the above material.

Here is the Link to Access the Lesson:

https://prealgebracoach.com/the-pythagorean-theorem/

This lesson is based around creating (Deriving) the Pythagorean Theorem together in class using GOLF!