Warm Up 03.23.12 Week 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.

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Presentation transcript:

Warm Up Week 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 2What is the measure of each inscribed angle? Red? Green? Blue? 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 If a right triangle is inscribed in a circle, then its hypotenuse is a diameter.

Circles – Inscribed Quadrilaterals Theorem A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.

Do 1: Assign ment: Handout – 10.3A Due at the end of the hour. Find the value of x.