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

AGENDA Notes on Circles Notes on Central Angles Homework Worksheet

Unit 3 Circles

Segments of Circles

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

CHORD: A segment whose endpoints are on the circle

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

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

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

Use P to determine whether each statement is true or false. Q R T S True: thumbs up False: thumbs down

Secant Line: intersects the circle at exactly TWO points

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

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

Central Arcs

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

Semicircle: An Arc that equals 180° To name: use 3 letters E D EDF P F

THINGS TO KNOW AND REMEMBER ALWAYS A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are Equal

measure of an arc = measure of central angle 96 Q m AB = 96° B C m ACB = 264° m AE = 84°

Arc Addition Postulate B m ABC = + m BC m AB

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

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”

Classwork Practice Worksheet

Homework: Practice Worksheet