Download Lesson 10

Geometry Chapter 10-4 notes
Inscribed Angles
Lesson 10-4 OBJECTIVE:
SWBAT find the measures of inscribed angles and the angles of inscribed polygons. In a previous lesson, you learned that a polygon that has its vertices on a circle is called an
inscribed polygon. Likewise, an ________________ is an angle that has its vertex on the
circle and its sides contained in chords of the circle.
If an angle is inscribed in a circle, then the measure of the angle
equals one-half the measure of its intercepted arc (or the
measure of the intercepted arc is twice the measure of the
inscribed angle).
Example #1 Measures of Inscribed Angles
If two inscribed angles of a circle (or congruent
circles) intercept congruent arcs or the same arc,
then the angles are congruent.
Example #2
Inscribed Arcs and Probability
If an inscribed angle intercepts a semicircle, the angle is a right angle.
Example #3
Angles of an Inscribed Triangle
If a quadrilateral is inscribed in a circle, then its opposite
angles are supplementary.