The triangle sum theorem states that the sum of all interior angles of a triangle is 180 degrees. To prove this, draw a line passing through one of the vertices of the triangle and parallel to the opposite side. This property of triangles states that the angles of a triangle always add up to 180°.
To prove the triangle sum theorem, consider a ∆ABC, as shown in the figure below. Draw a line parallel to the base of any triangle through its third vertex. Then, use transversals, vertical angles, and corresponding angles to rearrange those angle measures into a straight line, proving that they must add up to 180°.
To prove the triangle sum theorem, visualize yourself walking along the base of the triangle and measure the angles. If you connect three cities on a globe to form a triangle, and measure the angles, they’ll add up to more than 180 degrees! Visualize yourself walking along the base of the triangle and rotate by the amount of the internal angle.
Proof 1 uses the fact that alternate interior angles formed by a transversal with two parallel lines are congruent. Proof 2 uses the fact that a straight angle is 180° by putting two right angles together.
In conclusion, the triangle sum theorem states that the sum of interior angles of a triangle is 180 degrees. To prove this, draw a line parallel to one of the vertices of the triangle and use the triangle sum theorem to prove the triangle’s existence.
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