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Proving the Sum of Angles in a Triangle is 180°

This tutorial demonstrates how to prove that the sum of the angles in a triangle equals 180° using properties of parallel lines. We extend line AB to point G and draw line BE parallel to AC. By analyzing the angles formed, we establish that the angles on a straight line add up to 180°, leading to the conclusion that the sum of angles ∠CBA, ∠ACB, and ∠CAB equals 180°. Additionally, we explore the relationship between the exterior angle of a triangle and the sum of the two opposite interior angles.

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Proving the Sum of Angles in a Triangle is 180°

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  1. Geometric Proof GCSE Higher

  2. Prove that the sum of the angles in a triangle is 180° We can use previous knowledge of the properties of parallel lines C EXTEND the line AB to a point G E DRAW line BE parallel to AC A B G

  3. C E A B G Prove that the sum of the angles in a triangle is 180° Angles on a straight line <CBA + <CBE + <EBG = 180º <ACB = <CBE Alternate Angles SO <CBA + <ACB + <CAB = 180º <CAB = <EBG Corresponding Angles The Angle Sum of a triangle is 180º

  4. Using this … • …could you prove that the exterior angle of a triangle is equal to the sum of the two opposite interior angles?

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