Welcome to our exploration of one of geometry's most fundamental theorems. In any triangle, the sum of the three interior angles is always exactly 180 degrees. Today we'll discover why this is true through a beautiful geometric proof using parallel lines.
Let's start our proof by drawing any triangle ABC. We'll label the three interior angles as alpha, beta, and gamma. Our goal is to prove that the sum of these three angles equals exactly 180 degrees. This property holds for any triangle, regardless of its shape or size.
The crucial step in our proof is to draw a line d through vertex A that is parallel to side BC. This parallel line is the key that will unlock our proof. By creating this parallel line, we can use the properties of parallel lines and transversals to rearrange our angles.