Math 12 Page # of 2.

Topic: Cyclic Quadrilateral Theorem

Objective: The students will be able to use the Cyclic Quadrilateral Theorem to determine the measure of angles in a circle and to prove quadrilaterals are cyclic.

Number of Periods: 1 Page(s): 154 to 157


Review:

• have the students define what an inscribed polygon is (a polygon with its vertices on the side or sides of another object)

• e.g. Quadrilateral CDEF is inscribed in the circle.

Lesson:

• A set of points is called concyclic if all the points in the set lie on the same circle.

• e.g. Points C, D, E, and F are concyclic.


• Cyclic Quadrilateral Theorem (CQT)

1) A quadrilateral is cyclic if and only if the segment joi

ning two of the vertices subtends equal angles at the other two vertices on the same side of the segment.

In quadrilateral ABCD if, for instance, then ABCD is a cyclic quadrilateral. That means it is possible to construct a circle through the points A, B, C, and D.




Since quadrilateral BCDE is inscribed in a circle,

2) A quadrilateral is cyclic if and only if the opposite angles are supplementary.

In quadrilateral ABCD, if or then ABCD is a cyclic quadrilateral.




Since quadrilateral BCDE is cyclic,

and .





3) A quadrilateral is cyclic if and only if an exterior angle is equa

l to the interior opposite angle.

In quadrilateral ABCF, if then ABCF is a cyclic quadrilateral.








Since quadrilateral BCDE is cyclic, .

Oral Work: Pg. 157, #1a,b, #2, #3, #4a, #5

Home Work: Pg. 157, #1c, d, #4b, c, #6, #10, #13

Saved as Cyclic.Quadrilateral.Thm 2/6/99