Lesson 3 Menu 1.In, BD is a diameter and m AOD = 55. Find m COB. 2.Find m DOC. 3.Find m AOB....
27
1. In , BD is a diameter and mAOD = 55. Find mCOB. 2. Find mDOC. 3. Find mAOB. 4. Refer to . Find . 5. Find .
-
Upload
oswin-hodges -
Category
Documents
-
view
221 -
download
0
Transcript of Lesson 3 Menu 1.In, BD is a diameter and m AOD = 55. Find m COB. 2.Find m DOC. 3.Find m AOB....
1. In , BD is a diameter and
mAOD = 55. Find mCOB.
2. Find mDOC.
3. Find mAOB.
4. Refer to . Find .
5. Find .
• inscribed
• circumscribed
• Recognize and use relationships between arcs and chords.
• Recognize and use relationships between chords and diameters.
Prove Theorem 10.2
PROOF Write a two-column proof.
Prove:
Given:
is a semicircle.
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.
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
PROOF Choose the best reason to complete the following proof.
Prove:
Given:
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 .
A. A
B. B
C. C
D. D
A. Segment Addition Postulate
B. Definition of
C. Definition of Chord
D. Transitive Property
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?
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
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
Radius Perpendicular to a Chord
Since radius is perpendicular to chord
Arc addition postulate
Substitution
Substitution
Subtract 53 from each side.
Radius Perpendicular to a Chord
A radius perpendicular to a chord bisects it.
Definition of segment bisector
Draw radius Δ
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
Radius Perpendicular to a Chord
Answer: 4
Segment Addition Postulate
Subtract 6 from each side.
WJ = 6, WL = 10
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.
