1. Geometry Arcs and chords
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2. Warm Up
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3. Arcs and Chords A center 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 end points and all the points on the circle
between them.
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4. Arcs and Their Measure ARC MEASURE DIAGRAM A minor arc is an arc
whose points are on
or in the interior of a
center angle.
The measure of a minor arc
is equal to the measure of
its center angle.
A major arc is an arc
or in the exterior of a
The measure of a major arc
is equal to minus the measure of its center angle.
If the endpoints of an arc lie on a diameter,
the arc is a semicircle
The measure of a semicircle
is equal to A B C A B C
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5. The circle graph shows the types of music sold during one week at a music store.
Find A B C D E F G H
Other 26% M
Rock 25%
Rap 13%
Country 10%
Pop 13%
Jazz 13%
Classical 3%
R & B 11%
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6. Use the graph to find each of the following.
Now you try
Use the graph to find each of the following.
Classical 3% B C D E F G H
Other 26% M
Rock 25%
Rap 13%
Country 10%
Pop 13%
Jazz 13%
R & B 11%
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7. Adjacent arcs are arcs of the same circle that intersect at exactly one point. and are adjacent arcs. R S T
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8. Arc Addition Postulate
The measures of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. R S T
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9. Using the Arc Addition Postulate
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10. Now you try!
Find each measure.
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11. With in a circle or congruent circles, congruent arcs are
two arcs that have the same measure. In the figure,
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12. THEOREM A HYPOTHESIS CONCLUSION In a circle or congruent circles
1) Congruent central
angles have
congruent chords
2) Congruent chords have congruent arcs
3) Congruent arcs have
congruent central
angles.
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13. The converses of the parts of previous theorems are also true
The converses of the parts of previous theorems are also true. For example, with PART A, congruent chords have congruent central angles
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14. PART A
Proof:
Statements
Reasons
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15. Applying Congruent Angles, Arcs, and Chords
Find each measure. 1)
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16. 2)
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17. Now you try!
Find each measure 1) 2)
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18. is a radius (or diameter).
THEOREM B
HYPOTHESIS
CONCLUSION
1) In a circle, if a radius
(or diameter) is
perpendicular to
a chord, then it
bisects the chord
and its arc
2) In a circle, the
perpendicular
bisector of a chord
is a radius (or diameter).
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19. Using Radii and Chords
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20. 4) Find QR to the nearest tenth.
Now you try!
4) Find QR to the nearest tenth.
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21. Now some problems for you to practice.
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22. ASSESSMENT
1) The circle graph shows how a typical household spends money on energy. Find each of the following.
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23. Find each measure.
2) 139°
3) 270°
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27. REVIEW Arcs and Chords Arcs and Their Measure
DIAGRAM
A minor arc is an arc
whose points are on
or in the interior of a
center angle.
The measure of a minor arc
is equal to the measure of
its center angle.
A major arc is an arc
or in the exterior of a
The measure of a major arc
is equal to minus the measure of its center angle.
If the endpoints of an arc lie on a diameter,
the arc is a semicircle
The measure of a semicircle
is equal to A B C A B C
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28. The circle graph shows the types of music sold during one week at a music store.
Find A B C D E F G H
Other 26% M
Rock 25%
Rap 13%
Country 10%
Pop 13%
Jazz 13%
Classical 3%
R & B 11%
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29. Adjacent arcs are arcs of the same circle that intersect at exactly one point. and are adjacent arcs. R S T
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30. Arc Addition Postulate
The measures of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. R S T
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31. Using the Arc Addition Postulate
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32. With in a circle or congruent circles, congruent arcs are
two arcs that have the same measure. In the figure,
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33. THEOREM A HYPOTHESIS CONCLUSION In a circle or congruent circles
1) Congruent central
angles have
congruent chords
2) Congruent chords have congruent arcs
3) Congruent arcs have
congruent central
angles.
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34. PART A
Proof:
Statements
Reasons
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35. Applying Congruent Angles, Arcs, and Chords
Find each measure. 1)
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36. 2)
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37. is a radius (or diameter).
THEOREM B
HYPOTHESIS
CONCLUSION
1) In a circle, if a radius
(or diameter) is
perpendicular to
a chord, then it
bisects the chord
and its arc
2) In a circle, the
perpendicular
bisector of a chord
is a radius (or diameter).
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38. Using Radii and Chords
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39. You did a great job today!
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