Chapter 10: Properties of Circles

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Presentation transcript:

Chapter 10: Properties of Circles Section 10.3: Applying Properties of Chords

Section 10.3: Applying Properties of Chords Recall that a chord is a segment with both endpoints on a circle semi-circle

Chapter 10: Properties of Circles Theorem 10.3: In the same circle (or congruent circles), two minor arcs are congruent iff their corresponding chords are congruent

Chapter 10: Properties of Circles Example: If AB ≅ CD, what is the measure of AB?

Chapter 10: Properties of Circles Example: If mAB = 110, what is mBC? If mAC = 150, what is mAB?

Chapter 10: Properties of Circles What is the measure of CD? Arc BCD?

Chapter 10: Properties of Circles Bisecting Arcs If AB BC, then DB bisects ABC

Chapter 10: Properties of Circles Theorem: If a chord is a perpendicular bisector of another chord, then the first chord is a diameter

Chapter 10: Properties of Circles Example: For the following circles, is PR a diameter? If not, what could you change to make it a diameter?

Chapter 10: Properties of Circles Theorem: If a diameter of a circle is perpendicular to a chord, then the diameter is bisects the chord and its arc

Chapter 10: Properties of Circles Example For the following circles, PR is a diameter. Find the value of x.

Chapter 10: Properties of Circles Theorem: In the same circle (or in congruent circles), two chords are congruent iff they are equidistant from the center

Chapter 10: Properties of Circles Example For the following circles, find the value of x.

Chapter 10: Properties of Circles Homework: