Tag: sum of angles

Three proofs that the sum of angles of a triangle is 180

Theorem. The sum of the interior angles of any triangle is 180°. Here are three proofs for the sum of angles of triangles. Proof 1 uses the fact that the alternate interior angles formed by a transversal with two parallel lines are congruent. Proof 2 uses the exterior angle theorem. Proof 3 uses the idea…

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Theorems and Problems on Angles of Triangles

Here are three important theorems about triangles: sum of angles of a triangle, the measure of the exterior angle, and the base angles of an isosceles triangle. Sample problems where these are applied are also provided. The problems involved the concept of ratio. Theorem: The Sum of the Angles of a Triangle The sum of…

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Proofs of angle in a semicircle theorem

The Angle in a Semicircle Theorem states that the angle subtended by a diameter of a circle at the circumference is a right angle. An alternative statement of the theorem is the angle inscribed in a semicircle is a right angle. Proof Draw a radius of the circle from C. This makes two isosceles triangles….

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