Question Video: Using the Properties of Cyclic Quadrilaterals to Verify Whether the Given Trapezoid Is Cyclic | Nagwa Question Video: Using the Properties of Cyclic Quadrilaterals to Verify Whether the Given Trapezoid Is Cyclic | Nagwa

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

## Join Nagwa Classes

Attend live Mathematics sessions on Nagwa Classes to learn more about this topic from an expert teacher!

Is the trapezoid π΄π΅πΆπ· a cyclic quadrilateral?

02:04

### Video Transcript

Is the trapezoid π΄π΅πΆπ· a cyclic quadrilateral?

Letβs start by reminding ourselves that a cyclic quadrilateral is a quadrilateral whose vertices are inscribed on a circle. There are a few different angle properties that we can use to prove if a quadrilateral is cyclic or not.

Given that we have the diagonals marked, we may choose to use the property that 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. For example, if we could show that the angle π΄π·π΅ was equal in measure to angle π΄πΆπ΅, or indeed if we had another angle pair, for example, angle π·π΄πΆ equal to angle π·π΅πΆ, then the quadrilateral would be cyclic.

So letβs see if we can work out the angle measure of π΅πΆπ΄. Because weβre given that π΄π΅πΆπ· is a trapezoid, that means thereβll be one set of parallel sides. And we can see them here. Sides π΅πΆ and π΄π· are parallel. Therefore, angle π·π΅πΆ is alternate to this given angle of π΄π·π΅. And so theyβre both equal to 84 degrees.

Using the fact that the interior angles in a triangle add up to 180 degrees will allow us to find our unknown angle. We can write that the three angle measures of 84 degrees plus 52 degrees plus the measure of angle π΅πΆπ΄ is equal to 180 degrees. We can simplify this and then subtract 136 degrees from both sides, giving us that the measure of angle π΅πΆπ΄ is 44 degrees.

We can now really easily see that this angle measure of π΅πΆπ΄ is not equal to the angle measure at π΅π·π΄. Therefore, we can give the answer no, trapezoid π΄π΅πΆπ· is not a cyclic quadrilateral.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy