Dorchester2 - 03-04-2025-Arc Length and Area of Sectors

Presentation

•

Mathematics

•

9th - 12th Grade

•

Easy

Antoinette Norris Woodson

Used 2+ times

FREE Resource

14 Slides • 15 Questions

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Open Ended

Can you move these matches and change the number to sixteen?

How many moves are needed?

Be prepared to explain your reasoning to the class.

Type response here

Open Ended

Click on the image.

Type response here

~~● I can define the parts of a circle~~
● ~~I can define and measure in a circle~~
● ~~I can find the measure of segments of a circle~~
● I can discover the properties of tangent lines
● ~~I can find the measure of angles inside and outside of a circle~~
● I can find missing measures of angles and arcs using circle theorems.

● I can explain radian angle measures in terms of a circular radius and
arc length

Objectives

Circle Vocab

Draw

Line AB is tangent to circle O.

Segment AF is a diameter. The measure of arc AG = 100°.

The measure of arc CE = 30°.

The measure of arc m EF = 25°.

Draw the given information on the circle.

Use the given information and circle theorems to find the measure of < 1.

Draw

Line AB is tangent to circle O.

Segment AF is a diameter.

The measure of arc AG = 100°.

The measure of arc CE = 30°.

The measure of arc m EF = 25°.

Draw the given information on the circle.

Use the given information and circle theorems to find the measure of < 3.

Draw

Line AB is tangent to circle O.

Segment AF is a diameter.

The measure of arc AG = 100°.

The measure of arc CE = 30°.

The measure of arc m EF = 25°.

Draw the given information on the circle.

Use the given information and circle theorems to find the measure of < 6.

Draw

Line AB is tangent to circle O.

Segment AF is a diameter.

The measure of arc AG = 100°.

The measure of arc CE = 30°.

The measure of arc m EF = 25°.

Draw the given information on the circle.

Use the given information and circle theorems to find the measure of < 7.

Draw

Line AB is tangent to circle O.

Segment AF is a diameter.

The measure of arc AG = 100°.

The measure of arc CE = 30°.

The measure of arc m EF = 25°.

Draw the given information on the circle.

Use the given information and circle theorems to find the measure of < 8.

Draw

Find the measure of x.

Show your process.

Segment Lengths

https://youtu.be/aCdMntchnl0?feature=shared

Draw

Find x.

Show your process. Round to the nearest tenth.

Draw

Find x.

Show your process.

More about Arcs

https://study.com/academy/lesson/measure-of-an-arc.html

Arcs of a Circle

Minor Arc
Major Arc
Semicircle

Adjacent Arcs vs. Non-Adjacent Arcs

The measure of an arc is the degree of the angle that intercepts the arc. Remember that the measure of an arc is a degree, not a distance.
https://study.com/academy/lesson/measure-of-an-arc.html

Arc length is literally the length of the arc of a portion of a circle.
This arc is a part of the total circumference of a circle.
This length is measured as a linear distance.

https://study.com/academy/lesson/arc-length-definition-equation.html

Multiple Choice

Which proportion set up correctly for the figure?

$\frac{arc\ length}{8\pi}=\frac{225\degree}{360\degree}$

$\frac{arc\ length}{4\pi}=\frac{225\degree}{360\degree}$

$\frac{arc\ length}{16\pi}=\frac{225\degree}{360\degree}$

$\frac{arc\ length}{8\pi}=\frac{360\degree}{225\degree}$

Multiple Choice

Which proportion is set up correctly for the figure?

$\frac{arc\ length}{8\pi}=\frac{180\degree}{360\degree}$

$\frac{arc\ length}{4\pi}=\frac{180\degree}{360\degree}$

$\frac{arc\ length}{16\pi}=\frac{180\degree}{360\degree}$

$\frac{arc\ length}{360\degree}=\frac{4\pi}{180\degree}$

Multiple Choice

what is the arc length

5.23

103

33.33

Multiple Choice

If an exact arc length is

$\frac{4\pi}{7}$ , approximate the length to the nearest hundedth.

12.56

1.80

1.74

1.71

https://study.com/academy/lesson/finding-the-area-of-a-sector-formula-practice-problems.html

Central Angle

Central angles are angles with a vertex at the center of the circle.
Arcs are pieces of a circle's border. (crust of pizza/pie)
The measure of a central angle is equal to the measure of its intercepted arc.

Draw

Use what you know about circles vocabulary and theorems to solve for the missing angle.

Line AB is tangent to circle O.

Segment AF is a diameter.

The measure of arc AG = 100°.

The measure of arc CE = 30°.

The measure of arc EF = 25°.

Find the measure of angle 1.

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Dorchester2 - 03-04-2025-Arc Length and Area of Sectors

Circle Vocab

Segment Lengths

Arcs of a Circle

Adjacent Arcs vs. Non-Adjacent Arcs

​The measure of an arc is the degree of the angle that intercepts the arc. Remember that the measure of an arc is a degree, not a distance.https://study.com/academy/lesson/measure-of-an-arc.html

Central Angle

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

The measure of an arc is the degree of the angle that intercepts the arc. Remember that the measure of an arc is a degree, not a distance.
https://study.com/academy/lesson/measure-of-an-arc.html