Transcript Lesson 6.7 Lecture
Lesson 6.7
Arc Length
You have learned that the measure of a minor arc is equal to the measure of its
central angle.
On a clock, the measure of the arc from 12:00 to 4:00 is equal to the measure of the angle formed by the hour and minute hands. A circular clock is divided into 12 equal arcs, so the measure of each hour is
πππΒ° ππ
The measure of the arc from 12:00 to 4:00 is four times 30Β°, or 120Β°.
, or 30Β°. Notice that because the minute hand is longer, the tip of the minute hand must travel farther than the tip of the hour hand even though they both move 120Β° from 12:00 to
4:00.
So the arc length is different even though the arc measure is the same!
JRLeon Geometry Chapter 6.7
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Lesson 6.7
EXAMPLE 1
Arc Length
Letβs take another look at the arc measure.
What fraction of its circle is each arc?
Solution
ππΒ° πππΒ°
=
π π πππΒ° πππΒ°
=
π π πππΒ° πππΒ°
=
π π What do these fractions have to do with arc length? If you traveled halfway around a circle, youβd cover 1 2 of its perimeter, or circumference. If you went a quarter of the way 1 around, youβd travel ed of its circumference. The arc length is some fraction of the 4 circumference of its circle. The measure of an arc is calculated in units of degrees, but arc length is calculated in units of distance.
JRLeon Geometry Chapter 6.7
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Lesson 6.7
Arc Length
Arc Length Conjecture
The length of an arc equals the ( πππππππ ππ πππ πππ πππ
)
πͺ
C-66 Where C =
ο°
d or C = 2
ο°
r
EXAMPLE 2 Solution
JRLeon Geometry Chapter 6.7
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Lesson 6.7
EXAMPLE 3
Arc Length
C =
ο°
d or C = 2
ο°
r
Solution
JRLeon Geometry Chapter 6.7
HGSH
Lesson 6.7
Arc Length
C =
ο°
d or C = 2
ο°
r Intersecting Secants Conjecture
The measure of an angle formed by two secants that intersect outside a circle one-half the difference of the larger intercepted arc
measure and the smaller intercepted arc measure.
JRLeon Geometry Chapter 6.7
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Lesson 6.7
Arc Length
LESSON 6.7 : Pages 351-352, problems 1 through 10, 15.
JRLeon Geometry Chapter 6.5
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