Warm Up• Determine the measures of the indicated

angles.1.

2.

Now put it all together to solve for the missing angle.

INSCRIBED AND CIRCUMSCRIBED

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

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

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.

ExplorationUse 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!

Inscribed or Circumscribed?

• Describe the relationship between the polygon and the circle using “inscribed” and “circumscribed”?

Inscribed or Circumscribed?

• Describe the relationship between the polygon and the circle using “inscribed” and “circumscribed”?

Inscribed or Circumscribed?

• Describe the relationship between the polygon and the circle using “inscribed” and “circumscribed”?

Relationships

• Triangle Inscribed in a Circlehttp://www.geogebratube.org/student/m344117

• Triangle Circumscribed about a Circlehttp://www.geogebratube.org/student/m344105

Homework