Warm

1
Warm up
2.
2
Inscribed Angles

• Section 6.4

3
Standards

• MM2G3. Students will understand the properties of
  circles.
• b. Understand and use properties of central,
  inscribed, and related angles.

4
Essential Questions

• What are the important circle measurements?

5
Essential Questions

• How do I use inscribed angles to solve problems?
• How do I use properties of inscribed polygons?

6
Definitions

• Inscribed angle an angle whose vertex is on a
  circle and whose sides contain chords of the
  circle
• Intercepted arc the arc that lies in the
  interior of an inscribed angle and has endpoints
  on the angle

7
Measure of an Inscribed Angle Theorem

• If an angle is inscribed in a circle, then its
  measure is half the measure of its intercepted
  arc.

8
Example 1

• Find the measure of the blue arc or angle.

a.
b.
9
Congruent Inscribed Angles Theorem

• If two inscribed angles of a circle intercept the
  same arc, then the angles are congruent.

10
Example 2
11
Definitions

• Inscribed polygon a polygon whose vertices all
  lie on a circle.
• Circumscribed circle A circle with an inscribed
  polygon.

The polygon is an inscribed polygon and the
circle is a circumscribed circle.
12
Inscribed Right Triangle Theorem

• If a right triangle is inscribed in a circle,
  then the hypotenuse is a diameter of the circle.
  Conversely, if one side of an inscribed triangle
  is a diameter of the circle, then the triangle is
  a right triangle and the angle opposite the
  diameter is the right angle.

13
Inscribed Quadrilateral Theorem

• A quadrilateral can be inscribed in a circle if
  and only if its opposite angles are supplementary.

14
Example 3

• Find the value of each variable.

b.
a.
15
Practice

• Pages 207
• 2 18 even

16
Homework

• Page 209
• 2 26 even