Verify the Pythagorean Theorem: Is a Triangle with Sides 3, 4, and 5 Right-Angled?

To determine if the given triangle is right-angled, we will use the Pythagorean Theorem:

Step 1: Identify the sides and assign potential hypotenuse:
Assign $AC = 5$ as the hypotenuse since it is the longest side.

Step 2: Apply the Pythagorean Theorem:
According to the theorem, if the triangle is right-angled, it should satisfy:

$AB^2 + BC^2 = AC^2$

Substituting the given side lengths:

$3^2 + 4^2 = 5^2$

Calculate each square:

$9 + 16 = 25$

$25 = 25$

The equation holds true, confirming that the triangle is indeed right-angled.

Therefore, the solution to the problem is Yes.