10.2 Finding Arc Measures

What We Will Learn Find arc measure Identify congruent arcs

Needed Vocab Central angle: angle whose vertex is the center of the circle Minor arc: less than 180 degrees; uses two letters Major arc: greater than 180 degrees; uses three letters Semicircle: half a circle Measure of minor arc: measure of its related central angle Measure of major arc: difference of 360 degrees and related minor arc Adjacent arcs: two arcs that intersect at exactly one point Congruent circles: two or more circles with the same radius Congruent arcs: arcs whose central angles are congruent Similar arcs: arcs with same measure

Ex. 1 Finding Measures of Arcs Remember to read arcs in the order of the letters to see which arc they are talking about Remember two letters is a minor arc and three letters is a major arc A. arc RS 110° B. arc RTS 250° C. arc RST 180°

Ex. 2 Using Arc Addition Find each measure: A. arc GE 120° B. arc GEF 230° C. arc GF 130°

Ex. 3 Finding Measures of Arcs A recent survey asked teenagers whether they would rather meet a famous musician, athlete, actor, inventor, or other person. The circle graph shows the results. Find the indicated arc measures. A. arc AC 137° B. arc ACD 220° C. arc ADC 223° D. arc EBD 299°

Ex. 4 Identifying Congruent Arcs Tell whether the red arcs are congruent. Explain A. yes because same central angle of same circle B. no because although same central angle not congruent circles C. yes because same central angle and congruent circles because radius congruent