A circle can be named by its center using the  symbol. A circle with a center labeled C would be named  C. An unbroken part of a circle is called an.

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

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Presentation transcript:

A circle can be named by its center using the  symbol. A circle with a center labeled C would be named  C. An unbroken part of a circle is called an arc. 2 Types of arcs: 1.A minor arc of a circle is an arc that is shorter than half the circle and named by its endpoints. Circles 2.A major arc of a circle is an arc that is longer than half the circle and named by its endpoints and one other point on the arc.

P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters To name: use 3 letters  APB is a Central Angle

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

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

measure of an arc = measure of central angle A B C Q 96 m AB m ACB m AE E = = = 96° 264° 84°  EQA is a central angle.  EQA is ??°

Arc Addition Postulate A B C m ABC = m AB + m BC Arc Addition Postulate: The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

Tell me the measure of the following arcs. 80  100  40  140  A B C D R m DAB = m BCA = 240  260 

Identify congruent arcs Congruent circles are 2 circles with the same radius. Congruent arcs are 2 arcs with the same measure that are arcs of the same circle or of congruent circles.

RQ P 6 P Q R 12 