lesson 3 menu 1.in, bd is a diameter and m aod = 55. find m cob. 2.find m doc. 3.find m aob....
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1. In , BD is a diameter and
mAOD = 55. Find mCOB.
2. Find mDOC.
3. Find mAOB.
4. Refer to . Find .
5. Find .
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• inscribed
• circumscribed
• Recognize and use relationships between arcs and chords.
• Recognize and use relationships between chords and diameters.
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Prove Theorem 10.2
PROOF Write a two-column proof.
Prove:
Given:
is a semicircle.
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Prove Theorem 10.2
Proof:Statements Reasons
5. Def. of arc measure5.
4. Def. of arcs4.
2. Def. of semicircle2.
3. In a circle, if 2 chords are , corr. minor arcs are .
3.
Answer:
1. 1. Givenis a semicircle.
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Prove Theorem 10.2
Answer:
6. 6. Arc AdditionPostulate
7. 7. Substitution
8. 8. Subtraction Property and simplify
9. 9. Division Property
11. 11. Substitution
Statements Reasons
10. 10. Def. of arc measure
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PROOF Choose the best reason to complete the following proof.
Prove:
Given:
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Proof:Statements Reasons
1.
2.
3.
4.
1. Given
2. In a circle, 2 minor arcs are , chords are .
3. ______
4. In a circle, 2 chords are , minor arcs are .
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A. A
B. B
C. C
D. D
A. Segment Addition Postulate
B. Definition of
C. Definition of Chord
D. Transitive Property
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A regular hexagon is drawn in a circle as part of a logo for an advertisement. If opposite vertices are connected by line segments, what is the measure of angle P in degrees?
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Since connecting the opposite vertices of a regular hexagon divides the hexagon into six congruent triangles, each central angle will be congruent. The measure of each angle is 360 ÷ 6 or 60.
Answer: 60
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1. A
2. B
3. C
ADVERTISING A logo for an advertising campaign is
a pentagon that has five congruent central angles.
Determine whether
A. yes
B. no
C. cannot be determined
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Radius Perpendicular to a Chord
Since radius is perpendicular to chord
Arc addition postulate
Substitution
Substitution
Subtract 53 from each side.
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Radius Perpendicular to a Chord
A radius perpendicular to a chord bisects it.
Definition of segment bisector
Draw radius Δ
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Radius Perpendicular to a Chord
Use the Pythagorean Theorem to find WJ.
Pythagorean Theorem
Simplify.
Subtract 64 from each side.
Take the square root of each side.
JK = 8, WK = 10
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Radius Perpendicular to a Chord
Answer: 4
Segment Addition Postulate
Subtract 6 from each side.
WJ = 6, WL = 10
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Answer: PR = 9 and RH = 12
Chords Equidistant from Center
Draw to form a right triangle. Use the Pythagorean Theorem.
Pythagorean Theorem
Simplify.
Subtract 144 from each side.
Take the square root of each side.