1. 7.4 Cyclic Quadrilaterals

2. I) What is a Cyclic Quadrilateral
Quadrilateral: a polygon with four sides
Square, rectangle, parallelogram, trapezoid…..
The sum of all the interior angles is equal to 360 degrees
Cyclic Quadrilateral (CQ)
A quadrilateral with all four vertices (corners) on the circumference of the circle

3. EX: Find & Name all the CQ’s

4. II) Properties of a CQ
Opposite interior angles in a CQ add to 180 degrees
Then opposite angles must be “Supplementary”
If ABCD is a CQ
If opposite angles are “Supplementary”
Then ABCD must be a CQ

5. III) Proving Opposite Angles in a CQ Add to 180
Prove:

6. Exterior angles: angles created by the extension of one side
The Exterior angle is equal to the opposite interior angle
Exterior Angle

7. Practice:
Given: ABCD is a CQ
Prove:
Statement
Reason

8. EX: Determine the value of each angle

9. What is the value of “x+y”?

10. IV) Quadrilaterals & CQ’s
Four sides
Sum of all interior angles = 360 degrees
Not all quadrilaterals are CQ’s
Cyclic Quadrilaterals (CQ’s)
All 4 vertices are on the circumference
Opposite angles are suppl.
A quadrilateral can only be a CQ if opp. angles add to 180 degrees
NOTE: To prove that a quadrilateral is a CQ, then prove a pair of interior angles to be supplementary

11. Practice: Prove OACD is a CQ
Statement
Reason

12. Statement Reason Prove:
Given: G is the midpoint of AB E is the midpoint of AC
Prove:
Statement
Reason

13. Ex:
Statement
Reason

16. Given that ∆ABC is a right triangle and EDB is 90o
Given that ∆ABC is a right triangle and EDB is 90o. Prove that Angle DBE and ECD are equal.