To prove that a triangle is a right triangle, you can use something called the Pythagorean theorem.

So, what is this theorem?

It tells us that in a right triangle, the longest side (called the hypotenuse) squared is the same as the sum of the squares of the other two sides. You can write it like this:

$$c^2 = a^2 + b^2$$

In this formula:

• (c) is the length of the hypotenuse.
• (a) and (b) are the lengths of the other two sides.

To check if a triangle is a right triangle, follow these simple steps:

1. Measure the Sides: First, measure all three sides of the triangle. Let’s call these lengths (a), (b), and (c). Remember, (c) should be the longest side.

2. Use the Theorem: Now, plug these numbers into the Pythagorean theorem. You need to see if:

$$c^2 = a^2 + b^2$$

3. Check the Results: Calculate (a^2 + b^2) and compare it to (c^2):

   • If both sides are equal, then you have a right triangle.
   • If they are not equal, then it is not a right triangle.

Here’s a quick example to make it clear.

Imagine you have a triangle with sides measuring 3, 4, and 5.

• Let (a = 3), (b = 4), and (c = 5).
• Calculate (3^2 + 4^2): that’s (9 + 16 = 25).
• Then calculate (5^2): that’s also (25).

Since both results are the same (25 = 25), this triangle is a right triangle!

Using the Pythagorean theorem is a handy way to check if a triangle is a right triangle, and it’s a key idea in geometry.