Properties of Cyclic Quadrilaterals

This video tutorial explores the properties of cyclic quadrilaterals, focusing on the central angle theorem. It explains that opposite angles in a cyclic quadrilateral sum to 180 degrees, using the central angle theorem to prove this. The lesson includes a step-by-step proof and verification with additional angles, emphasizing that this property is unique to cyclic quadrilaterals. The tutorial concludes with a summary of key takeaways.

What is a cyclic quadrilateral?

• A quadrilateral with one pair of parallel sides

• A quadrilateral with opposite angles equal

• A quadrilateral with all vertices on a circle

• A quadrilateral with all sides equal

According to the central angle theorem, how is the inscribed angle related to the central angle?

• The inscribed angle is half the central angle

• The inscribed angle is twice the central angle

• The inscribed angle is equal to the central angle

• The inscribed angle is unrelated to the central angle

What do opposite angles in a cyclic quadrilateral sum to?

• 90 degrees

• 180 degrees

• 270 degrees

• 360 degrees

If the measure of arc BCD is 2x, what is the measure of angle x in a cyclic quadrilateral?

• x = 1/2 * measure of arc BCD

• x = 2 * measure of arc BCD

• x = measure of arc BCD

• x = 1/4 * measure of arc BCD

How do you find the sum of angles x and y in a cyclic quadrilateral?

• x + y = 90 degrees

• x + y = 180 degrees

• x + y = 270 degrees

• x + y = 360 degrees

What is the sum of angles q and r in a cyclic quadrilateral?

• 90 degrees

• 360 degrees

• 180 degrees

• 270 degrees

Why do the angles in a quadrilateral sum to 360 degrees?

• Because it is a property of all polygons

• Because it is a property of all quadrilaterals

• Because it is a property of cyclic quadrilaterals

• Because it is a property of triangles

What is unique about the theorem discussed in the lesson?

• It applies only to cyclic quadrilaterals

• It applies only to triangles

• It applies to all quadrilaterals

• It applies to all polygons

Which of the following is NOT true about cyclic quadrilaterals?

• All sides are equal

• The central angle is twice the inscribed angle

• Opposite angles sum to 180 degrees

• All vertices lie on a circle

What must be true for the theorem about opposite angles to hold?

• The quadrilateral must be a rhombus

• The quadrilateral must be a square

• The quadrilateral must be a rectangle

• The quadrilateral must be cyclic