Welcome! Today we'll discover one of the most fundamental properties in geometry: the sum of angles in a triangle. Every triangle, no matter its shape or size, has three interior angles. Let's call them alpha, beta, and gamma.
Now let's imagine we can cut out each angle from our triangle. We'll take angle alpha from vertex A, angle beta from vertex B, and angle gamma from vertex C. Watch as we extract these angle pieces.
Now watch what happens when we arrange these three angles together at a single point. We place alpha, then beta, then gamma right next to each other. Amazing! Together they form exactly a straight line, which measures one hundred eighty degrees.
This amazing property works for every single triangle! Whether it's an equilateral triangle with all sides equal, a right triangle with a ninety degree angle, or any other triangle shape, the sum of the three interior angles is always exactly one hundred eighty degrees. This is a fundamental law of geometry.
To summarize what we've learned: The sum of all interior angles in any triangle is always one hundred eighty degrees. This applies to every triangle, no matter its shape or size. When we arrange the three angles together, they form a perfect straight line. This is one of the most important and fundamental principles in geometry.