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Published byJagger Cogdill Modified over 2 years ago

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**How do we use angle measures to find measures of arcs?**

CCGPS Geometry UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MMC9-12.G.C.1-5,G.GMD.1-3 Today’s Question: How do we use angle measures to find measures of arcs? Standard: MMC9-12.G.C.2

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AGENDA Notes on Circles Notes on Central Angles Homework Worksheet

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Unit 3 Circles

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Segments of Circles

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Parts of a Circle Circle – set of all points _________ from a given point called the _____ of the circle. equidistant C center Symbol: C

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CHORD: A segment whose endpoints are on the circle

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Radius RADIUS: Distance from the center to point on circle P

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**Distance across the circle through its center**

Diameter DIAMETER: Distance across the circle through its center P Also known as the longest chord.

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D = ? 24 32 12 r = ? 16 r = ? 4.5 6 D = ? 12 9

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**Use P to determine whether each statement is true or false.**

Q R T S True: thumbs up False: thumbs down

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Secant Line: intersects the circle at exactly TWO points

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**a LINE that intersects the circle exactly ONE time**

Tangent Line: a LINE that intersects the circle exactly ONE time Forms a 90°angle with a radius Point of Tangency: The point where the tangent intersects the circle

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**Secant Radius Diameter Chord Tangent**

Name the term that best describes the notation. Secant Radius Diameter Chord Tangent

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Central Arcs

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**Central Angle : An Angle whose vertex is at the center of the circle**

Major Arc Minor Arc More than 180° Less than 180° ACB P AB To name: use 3 letters C To name: use 2 letters B APB is a Central Angle

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**Semicircle: An Arc that equals 180°**

To name: use 3 letters E D EDF P F

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**THINGS TO KNOW AND REMEMBER ALWAYS**

A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are Equal

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**measure of an arc = measure of central angle**

96 Q m AB = 96° B C m ACB = 264° m AE = 84°

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**Arc Addition Postulate**

B m ABC = + m BC m AB

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**240 260 m DAB = m BCA = Tell me the measure of the following arcs. D**

140 260 m BCA = R 40 100 80 C B

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CONGRUENT ARCS Congruent Arcs have the same measure and MUST come from the same circle or of congruent circles. C B D 45 45 110 A Arc length is proportional to “r”

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Classwork Practice Worksheet

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Homework: Practice Worksheet

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