Warm Up
• Determine the measures of the indicated
angles.
1.
2.
Now put it all together to solve for the missing
angle.
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.
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!
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 Circle
http://www.geogebratube.org/student/m34411
7
• Triangle Circumscribed about a Circle
http://www.geogebratube.org/student/m34410
5
Homework