Category: Geometry

Tangents to Circles Problems

Problem 1 The figure below shows circle A and rectangle ABCD. The measures of segments are indicated. How long is EB? This problem is not that hard. All you need to see is that AB and AE are radius of Circle A. Also, because ABCD is a rectangle, BD = AC. Now, all you need…

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Geometric Interpretation of Trapezoid Area Formula

Problem 1 Show that the area of a trapezoid (trapezium) is half its height times the sum of the parallel sides. Solution Cut the trapezoid along the midpoints of the pair of non-parallel side. This halves its height. Rotate one of the parts 180 degrees about a midpoint. In the figure below, it’s about the…

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Proof of Triangle Exterior Angle Theorem

The exterior angle of a triangle is the angle that forms a linear pair with an interior angle of the the triangle. To draw the exterior angle all you need to do is to extend the side of the triangle. A linear pair is a pair of angle that forms a straight line. In the figure…

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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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