FIND ARC MEASURES

10.2

Vocab

Central Angle: an angle where the vertex is at the center of the circle.

And the vocab continues

Minor arc: an angle inside a circle whose measure is less than 180°. (They only need 2 letters to be named but can also have 3 letters.)

Major arc: an angle inside a circle whose measure is greater than 180° or the arc that is not the minor arc. (They require 3 letters to be named)

Semicircle: Half a circle

Name the minor and major arc

AB

ADB

I’m a major!

I’m a minor!

Arc Addition postulate

This theorem allows us to add arcs

Find the indicated arc

Find the indicated arc

360 – 90 = 270º360 – 90 = 270º

Find the indicated arc

360 360 ÷3 ÷3 = 120º= 120º

Finding measures of arcs, where EB is a diameter

75º

180-35 = 145º75 + 35 = 110º360 – 110 = 250º

75o

35o

Word Problems

306360 – 306 = 54º

54º

180 +54 = 234º

180º

306o

Congruency

Circles are said to be congruent if and only if their radii are the same.

Arcs are considered to be congruent if they are the same measure and the circles they are contained in are also congruent.

2 arcs of the same measure in the same circle are considered congruent.

Congruent?

Congruent?

= 124.5 = 124.5

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