Question Video: Using the Properties of Cyclic Quadrilaterals to Verify Whether a given Quadrilateral Is a Cyclic | Nagwa Question Video: Using the Properties of Cyclic Quadrilaterals to Verify Whether a given Quadrilateral Is a Cyclic | Nagwa

# Question Video: Using the Properties of Cyclic Quadrilaterals to Verify Whether a given Quadrilateral Is a Cyclic Mathematics • Third Year of Preparatory School

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### Video Transcript

Letβs recall that a cyclic quadrilateral is a four-sided polygon whose vertices are inscribed on a circle. We can prove that a quadrilateral is cyclic or not by using a few different properties. However, we can observe in π΄π΅πΆπ· that weβre given the diagonals. If an angle created by a diagonal and side is equal in measure to the angle created by the other diagonal and opposite side, then the quadrilateral is cyclic. If these angle measures are not equal, then it is not a cyclic quadrilateral.

So, letβs look at this angle πΆπ·π΅. Itβs an angle created by a diagonal and a side. The angle created by the other diagonal and opposite side would be this angle πΆπ΄π΅. And of course 82 degrees is not equal to 78 degrees. Therefore, the measure of angle πΆπ·π΅ is not equal to the measure of angle πΆπ΄π΅.

We can then give the answer no, since π΄π΅πΆπ· is not a cyclic quadrilateral.

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