12 2 Arcs and Chords Objectives Apply properties

12 -2 Arcs and Chords Objectives Apply properties of arcs. Apply properties of chords. Holt Mc. Dougal Geometry

12 -2 Arcs and Chords A _______is an angle whose vertex is the center of a circle. An ____ is an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them. Holt Mc. Dougal Geometry

12 -2 Arcs and Chords Holt Mc. Dougal Geometry

12 -2 Arcs and Chords Writing Math Minor arcs may be named by two points. Major arcs and semicircles must be named by three points. Holt Mc. Dougal Geometry

12 -2 Arcs and Chords Example 1: Data Application The circle graph shows the types of grass planted in the yards of one neighborhood. Find m. KLF. Holt Mc. Dougal Geometry

12 -2 Arcs and Chords _________ are arcs of the same circle that intersect at exactly one point. RS and ST are adjacent arcs. Holt Mc. Dougal Geometry

12 -2 Arcs and Chords Example 2 a: Using the Arc Addition Postulate Find m. BD. Holt Mc. Dougal Geometry

12 -2 Arcs and Chords Example 2 b Find each measure. m. JKL Holt Mc. Dougal Geometry

12 -2 Arcs and Chords Example 2 c Find each measure. m. LJN Holt Mc. Dougal Geometry

12 -2 Arcs and Chords Within a circle or congruent circles, __________ are two arcs that have the same measure. In the figure ST UV. Holt Mc. Dougal Geometry

12 -2 Arcs and Chords Holt Mc. Dougal Geometry

12 -2 Arcs and Chords Example 3 A: Applying Congruent Angles, Arcs, and Chords TV WS. Find m. WS. Holt Mc. Dougal Geometry

12 -2 Arcs and Chords Example 3 B: Applying Congruent Angles, Arcs, and Chords C J, and m GCD m NJM. Find NM. Holt Mc. Dougal Geometry

12 -2 Arcs and Chords Holt Mc. Dougal Geometry

12 -2 Arcs and Chords Example 4: Using Radii and Chords Find NP. Step 1 Draw radius RN. Step 2 Use the Pythagorean Theorem. Step 3 Find NP. Holt Mc. Dougal Geometry