SECTION 10.4Inscribed Angles

INSCRIBED ANGLES

How do I find the measure of an inscribed angle?

How do I find the measures of the angles of an inscribed polygons?

INSCRIBED ANGLE

Inscribed Angle: Angle with the vertex on the circle and the sides are chords.

Intercepted Arc: The arc created by the chords.

INSCRIBED ANGLE

Inscribed and central angles are different!

Inscribed =

Central =

INTERCEPTED ARCS

Which are the intercepted Arcs?

Inscribed =

Central =

THEOREM 10.4

Inscribed Angle Theorem – If an angle is inscribed in a circle, then the measure of the angle is ½ the measure of the intercepted arc.

A

B

C

D

THEOREM 10.4

If what is ?

If 48,what is ?

If = 230,what is ?

A

B

C

D

EXAMPLE

In F, = 20, = 40, = 108, and . Find the measures of the numbered angles.

THEOREM

Theorem 10.6: If two inscribed angles of a circle intercept congruent arcs or the same arc, then the angles are congruent.

A B

CD

A B

CD

THEOREM

Theorem 10.7: If an inscribed angle intercepts a semicircle, the angle is a right angle.

EXAMPLE

Triangles TVU and TSU are inscribed in with . Find the measure of each numbered angle if and .

THEOREM

Theorem 10.8: If a quadrilateral is inscribed in a circle, then its opposite angle are supplementary.

EXAMPLE

Quadrilateral QRTS is inscribed in M. If = 87 and = 102. Find and .

HOMEWORK

Page 549 #8, 10, 14 – 30 Even

LESSON PLAN

Intro Add a new angle inside a circle, an inscribed

angle. Then develop theorems about inscribed angles.

Standards- 9. Supplies – slides, whiteboard, note sheets Timing: One day for notes, one day for a

combined review of 10.3 and 10.4 and a quiz. Day 1:

Essential Questions- slides 2 Input-slides 3, 6, 9 – 11, 13 Guided Practice - slides 4, 5, 7, 8, 12, 14 Independent Practice – Book Work