1. Warm Up Determine the measures of the indicated angles. 1. 2.
Now put it all together to solve for the missing angle.

2. Inscribed and Circumscribed
Unit 6 – Day 3
Inscribed and Circumscribed

3. Today’s Objectives
Students will use properties of Central angles and Tangent lines to solve for missing parts
Students will define inscribed and circumscribed polygons
Students will explore properties of Inscribed and Circumscribed Triangles and Quadrilaterals

4. Using Properties of Central Angles and Tangent Lines
Use the properties of Tangent Lines, Central Angles, and Inscribed Angles to solve for the missing parts

5. Defining Inscribed and Circumscribed Polygons Guided Notes
Definitions
Inscribed: A polygon is inscribed in a circle if all of the vertices lie on the circle.
Circumscribed: A polygon is circumscribed about a circle if each side is tangent to the circle.

6. Exploration
Use the properties of inscribed angles to find the missing angles
Given: m∠ADC=60˚, mBC=40˚and mCD=110˚, find m∠ABC. Then find m∠BCD and m∠DAB
m∠ABC =_________
m∠BCD =_________
m∠DAB =_________
What do you notice about opposite angles in the quadrilateral?
Supplementary
About the sum of all angles?
360º
Therefore, opposite angles of an inscribed quadrilateral are supplementary!

7. Inscribed or Circumscribed?
Describe the relationship between the polygon and the circle using “inscribed” and “circumscribed”?

8. Inscribed or Circumscribed?
Describe the relationship between the polygon and the circle using “inscribed” and “circumscribed”?

9. Inscribed or Circumscribed?
Describe the relationship between the polygon and the circle using “inscribed” and “circumscribed”?

10. Relationships Triangle Inscribed in a Circle
Triangle Circumscribed about a Circle

11. Homework