Geometry Lesson 10.2.notebook

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Measuring Angles and Arcs

Central Angle of a Circle ­ an angle with a vertex in the center of the circle and its sides are radii of the circle.

Remember that there are 360 degrees in a circle.

Sum of Central Angles ­ The sum of the measures of the central angles of a circle with no interior points in common is 360.

Find x.

Geometry Lesson 10.2.notebook

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Try. Find x for each.

a. b.

ARC ­ a portion of a circle defined by two endpoints.

The symbol for an arc is PR

Geometry Lesson 10.2.notebook

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Minor Arc ­ The measure of a minor arc is less than 180 and equal to its related central angle.

Major Arc ­ The measure of a major arc is greater than 180 and equal to 360 minus the measure of the minor arc with the same endpoints.

Semicircle ­ an arc with endpoints that lie on a diameter.

When naming a minor arc, we usually only name it using its endpoints.

When naming a major arc, we use 3 points, the two endpoints and a point between those endpoints on the arc.

ADB

When naming a semicircle, we use 3 letters, the two endpoints and a point in between to signify which semicircle we are talking about.

Geometry Lesson 10.2.notebook

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May 14, 2015

a. MQ

b. MNP

c. MNQ

Congruent Arcs ­ arcs in the same or congruent circles that have the same measure.

Geometry Lesson 10.2.notebook

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Female Participation in Sports

Refer to the circle graph. Find each measure.

a.

Since volleyball is 18% of the graph and theentire graph is 360 degrees;

b.

c.

d.

Adjacent Arcs ­ arcs in a circle with exactly one point in common.

Geometry Lesson 10.2.notebook

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Arc Addition Postulate ­ The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

Find the measure of each arc.

a.

b.

c.

d.

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Arc Length ­ the distance between the endpoints along an arc measured in linear units.

The ratio of the length of an arc l to the circumference of the circle is equal to the ratio of the degree measure of the arc to 360.

Proportion

Equation

Find the length of

a. b.

Geometry Lesson 10.2.notebook

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P. 696 12 ­ 44 evens, 45 ­ 51 all

One last thing, if the problem asks to find PS, you will be finding arc length.

If it asks you to find the mPS, you are finding angle measure.