Warm Up 03.23.12Week 1

Section 10.3 Day

1

I will use inscribed angles to solve problems.

Inscribed Angles

An angle whose vertex is on a circle and whose sides contain chords.

Intercepted Arc Arc that lies in the interior of an inscribed angle.

Measure of an Inscribed Angle

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

Theorem 10.8

Ex 1

a.

b.

c.

180°

230°

50°

Ex 2 What is the measure of each inscribed angle?

Red?

Green?

Blue?

30°

30°

30°

Arcs – Multiple Inscribed Angles

Theorem 10.9 If two inscribed angles of a circle intercept the same arc,

then the angles are congruent.

Ex 3 Find the value of x.

Circles – Inscribed Right Triangles

Theorem 10.10 If a right triangle is inscribed in a circle,

then its hypotenuse is a diameter.

Circles – Inscribed Quadrilaterals

Theorem 10.11 A quadrilateral can be inscribed in a circle if and only if its

opposite angles are supplementary.

Do 1:

Assignment:

Handout – 10.3A Due at the end of the hour.

Find the value of x.