9.3 Arcs and Central Angles

Objectives At the completion of the lesson, you will be able to… Define and identify arcs and central angles in circles Calculate the measures of arcs and central angles in circles

Using Arcs of Circles Central Angle – an angle whose vertex is at the center of a circle Major Arc – formed by two points on a circle and its measure is greater than 180; named with 3 endpoints Minor Arc – formed by two points on a circle whose measure is less than 180; named with 2 endpoints Semicircle – an arc formed by two points on a circle whose measure is equal to 180

Example: Naming Arcs Name: B minor arcs: major arcs: semicircles: An acute central angle: Two congruent arcs: 60° 60° B 180°

Measuring arcs Measure of an arc: equal to the measure of an arc’s central angle Minor arc: Major arc – think about it: how would I find 60° 60° B 180°

A postulate m = m + m Arc Addition Postulate The measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs. m = m + m

Ex. 1: Finding Measures of Arcs Find the measure of each arc of R. 80°

Ex. 2: Finding Measures of Arcs Find the measure of each arc. 40° 80° 110°

Congruent arcs and are in the same circle and m = m = 45°. So,  Arcs, in the same circle or in congruent circles, that have equal measures 45° 45° and are in the same circle and m = m = 45°. So, 

Homework Page 341 Classroom exercises 1-13 Page 341 Written Exercises 1-8 Quiz tomorrow on 9.1-9.3