Subjects geometry

Triangle Angle Sum 0D5279

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Triangle Angle Sum 0D5279


1. The problem is to prove that the sum of the interior angles of a triangle is 180 degrees. 2. According to the Midpoint Line Theorem (MDLB theorem), a line drawn through the midpoint of one side of a triangle and parallel to another side creates a smaller triangle similar to the original. 3. Consider triangle ABC. Let D be the midpoint of side BC. Draw line DE parallel to side AB. 4. By the properties of parallel lines, angle ADE equals angle BAC (corresponding angles), and angle AED equals angle ABC. 5. The angles on a straight line at point D sum to 180 degrees: angle ADE + angle ADC + angle CDE = 180 degrees. 6. Since angle ADE = angle BAC and angle CDE = angle ABC, and angle ADC is angle ACB, the sum of angles BAC + ABC + ACB = 180 degrees. 7. Therefore, the sum of the interior angles of triangle ABC is 180 degrees. This completes the proof using the Midpoint Line Theorem.