The Proof of the Cyclic Quadrilateral Theorem

A cyclic quadrilateral is a quadrilateral inscribed in a circle. A polygon that is inscribed in a circle is a polygon whose vertices are on the circle. Some of the inscribed polygons are shown in the next figure. In this post, we are going to show a special property of one inscribed polygon which is […]
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Proof That the Angle Sum of a Pentagram is 180 Degrees

A pentagram is a five pointed star as shown below. In this post, we are going to learn two proofs that the angle sum of a pentagram is equal to 180 degrees. ┬áIn the discussion below, we will refer to the angles at the 5 angles at the tip of the pentagram. Proof 1: Inscribing […]
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The Proof of the Third Case of the Inscribed Angle Theorem

This is the third and the last case of the Proofs of the Inscribed Angle Theorem. In the first case, we used an auxiliary line between the sides of the angles to come up with the proof. In the second case, we drew a line segment from the center to the intersection of the circle […]
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