## Tapping It Up a Notch: Pythagorean Theorem – Part 3

In the first part, we used an inquiry/discovery approach to help students visualize how Pythagorean Theorem works, then followed that with a visualization of the general proof / derivation of the formula to show how we can find the hypotenuse of a right-angle triangle when given the lengths of the two legs.

In this post, we will now make a connection between the **visual representation** of the **Pythagorean Theorem** with the **algebraic representation** to show students that the intent of algebra is not to confuse, but rather to make calculations more easily when patterns have been generalized as they have here.

## Using Pythagorean Theorem to Find the Length of the Hypotenuse

### Connecting the Visual Representation and Algebraic Representation

In this video, we now attempt to make a connection between the visual representation and algebraic representation for a specific right-angle triangle. Ensuring students have already watched the first video and second video from part one and part two of this series is important to maximize the effectiveness.

## Summary of Pythagorean Theorem Video

### Start With A Specific Example: Visually and Algebraically

We now start with variables representing the side lengths of 6 metres and 8 metres in an attempt to find the length of the hypotenuse.

### Connect Squaring Side-Lengths to Area Visually and Algebraically

We show that squaring the side lengths on the right-angle triangle will yield an area since we are multiplying length by width (or side by side, in this case).

### Evaluate Squaring The Length of the Legs

Squaring 6 m and 8 m yields areas of 36 m^2 and 64 m^2, respectively. This is shown algebraically as well as visually:

### Show The Sum of the Squares of the Leg Lengths

We now calculate the sum of the two squares, 36 m^2 plus 64 m^2 which gives the result of 100 m^2. We show what this looks like in the formula as well as visually.

### Square-Root to Determine the Side Lengths

In order to determine the side length of the hypotenuse square, we must now square-root. This is a great place to discuss opposite operations and make the connection between square-rooting 100 m^2 as well as c^2.

### Final Result of 10 m for the Length of the Hypotenuse

Square-rooting both sides of the equation as well as the visual representation will give the result of 10 m for the length of the hypotenuse.

What are your thoughts? How can we improve these videos to better assist students understanding how the algebraic representation of Pythagorean Theorem works? Leave a comment below!

## Other Related Pythagorean Theorem Posts:

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## About Kyle Pearce

I’m Kyle Pearce and I am a former high school math teacher. I’m now the K-12 Mathematics Consultant with the Greater Essex County District School Board, where I uncover creative ways to spark curiosity and fuel sense making in mathematics. Read more.

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