The Pythagorean Theorem - More Than Just Right Triangles!

Paijar Team

Thu, 21 Nov 2024

Hey mathletes! Today, we're diving into a classic: the Pythagorean Theorem. You might know it as the formula for right triangles (a^2 + b^2 = c^2), but this theorem has some surprising applications!

The Basics:

Imagine a right angled triangle. The Pythagorean Theorem tells us that the square of the hypotenuse (the longest side, opposite the right angle) is equal to the sum of the squares of the other two sides.

Beyond Triangles:

This theorem isn't just for triangles! It can be used to solve problems involving distances in squares, rectangles, and even 3D shapes. Here's an example:

Imagine a square with side length "a." The diagonal (line connecting opposite corners) will split the square into two right triangles. The diagonal will have a length of "a√2" (a times the square root of 2). How did we get this?

Think about one of the right triangles formed by the diagonal. Each of the shorter sides (half the diagonal) has a length of "a/√2" (a divided by the square root of 2). Using the Pythagorean Theorem, we get:

(a/√2)^2 + (a/√2)^2 = (diagonal)^2

which simplifies to a^2/2 + a^2/2 = a^2 * 2, and finally a^2 = (diagonal)^2 / 2, so the diagonal is a√2.

The Takeaway:

The Pythagorean Theorem is a powerful tool that goes beyond right triangles. It helps us understand relationships between sides and diagonals in various shapes. So next time you see a square or rectangle, remember – there might be a hidden Pythagorean connection waiting to be discovered!

The Challenge:

Here’s a worksheet of the Pythagorean Theorem! Solve it and let us know the answers in the comment section. If you feel you need more in depth knowledge and lessons on the Pythagorean Theorem then watch our expert teachers’ video lessons on this topic!