To prove that the sum of the measures of the interior angles of a triangle is always 180 degrees, you would typically use alternate interior angles.
Here's a brief explanation of how this works:
- Consider a triangle with angles A, B, and C.
- Extend one side of the triangle and draw a line parallel to that side through the opposite vertex.
- The angles formed between the line you drew and the sides of the triangle correspond to the angles within the triangle.
- By the properties of alternate interior angles, the angle at the vertex where the triangle's two sides meet is equal to the angle created at the parallel line, leading to the conclusion that the sum of the angles in the triangle equals the angles formed on the line, which sums to 180 degrees.
Thus, the concept that best fits the proof you are looking for is alternate interior angles.
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