11-2 Arcs and Chords Warm Up Lesson Presentation Lesson Quiz Holt Geometry

Objectives Apply properties of arcs. Find the Circumference of Circles.

Vocabulary central angle semicircle arc adjacent arcs minor arc congruent arcs major arc

Note 70 A central angle is an angle whose vertex is the center of a circle. An arc is an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them.

Example 1: Data Application The circle graph shows the types of grass planted in the yards of one neighborhood. Find mKLF.

Check It Out! Example 1 Use the graph to find each of the following. a. mFMC b. mAHB c. mEMD

Adjacent arcs are arcs of the same circle that intersect at exactly one point. RS and ST are adjacent arcs.

Example 2: Using the Arc Addition Postulate Find mBD.

Check It Out! Example 2a Find each measure. mJKL

Check It Out! Example 2b Find each measure. mLJN

Within a circle or congruent circles, congruent arcs are two arcs that have the same measure. In the figure ST  UV.

The Circumference of a circle can be found by using on of the formulas: C = 2pr or C = pd

Find the circumference of circle P if JM = 12cm

The length of an arc is a fraction of the circumference of the circle.

Example 4A: Finding Arc Length Find each arc length. Give answers in terms of . FG

Example 4B: Finding Arc Length Find each arc length. Give answers in terms of . an arc with measure 62 in a circle with radius 2 m

Check It Out! Example 4a Find each arc length. Give your answer in terms of . GH

Lesson Quiz: Part I 1. The circle graph shows the types of cuisine available in a city. Find mTRQ. 158.4

Lesson Quiz: Part III Find each measure. Give answers in terms of  2. Length of NP 3. Circumference of circle Q 4. Measure of LMP