Connect Visual to Algebraic Representation of Pythagorean Theorem

Tapping It Up a Notch: Pythagorean Theorem – Part 3

Pythagorean Theorem - Visual of 6-squared and 8-squared

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.

Connecting the Visual and Algebraic Representations of Pythagorean Theorem

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).

Pythagorean Theorem - Visual of 6-squared and 8-squared

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:

Pythagorean Theorem - Simplifying 6-squared and 8-squared

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.

Pythagorean Theorem - Simplify by Adding a-squared plus b-squared

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.

Pythagorean Theorem - Square root both sides of the equation

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.

Pythagorean Theorem - Find the side lengths of the hypotenuse square

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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