Lesson 3 Menu 1.In, BD is a diameter and m  AOD = 55. Find m  COB. 2.Find m  DOC. 3.Find m  AOB. 4.Refer to. Find. 5.Find.

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Presentation transcript:

Lesson 3 Menu 1.In, BD is a diameter and m  AOD = 55. Find m  COB. 2.Find m  DOC. 3.Find m  AOB. 4.Refer to. Find. 5.Find.

Lesson 3 MI/Vocab inscribed circumscribed Recognize and use relationships between arcs and chords. Recognize and use relationships between chords and diameters.

Lesson 3 TH1

Lesson 3 Ex1 Prove Theorem 10.2 PROOF Write a two-column proof. Prove: Given: is a semicircle.

Lesson 3 Ex1 Prove Theorem 10.2 Proof: StatementsReasons 5. Def. of arc measure Def. of arcs4. 2. Def. of semicircle In a circle, if 2 chords are, corr. minor arcs are. 3. Answer: Given is a semicircle.

Lesson 3 Ex1 Prove Theorem 10.2 Answer: 6. 6.Arc Addition Postulate 7. 7.Substitution 8. 8.Subtraction Property and simplify 9.9.Division Property Substitution StatementsReasons Def. of arc measure

Lesson 3 CYP1 PROOF Choose the best reason to complete the following proof. Prove: Given:

Lesson 3 CYP1 Proof: Statements Reasons 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 Lesson 3 CYP1 A.Segment Addition Postulate B.Definition of  C.Definition of Chord D.Transitive Property

Lesson 3 Ex2 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?

Lesson 3 Ex2 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 Lesson 3 CYP2 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

Lesson 3 TH2

Lesson 3 Ex3 Radius Perpendicular to a Chord

Lesson 3 Ex3 Radius Perpendicular to a Chord Since radius is perpendicular to chord Arc addition postulate Substitution Subtract 53 from each side.

Lesson 3 Ex3 Radius Perpendicular to a Chord

Lesson 3 Ex3 Radius Perpendicular to a Chord A radius perpendicular to a chord bisects it. Definition of segment bisector Draw radius Δ

Lesson 3 Ex3 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

Lesson 3 Ex3 Radius Perpendicular to a Chord Answer: 4 Segment Addition Postulate Subtract 6 from each side. WJ = 6, WL = 10

1.A 2.B 3.C 4.D Lesson 3 CYP3 A.35 B.70 C.105 D.145

1.A 2.B 3.C 4.D Lesson 3 CYP3 A.15 B.5 C.10 D.25

Lesson 3 TH3

Lesson 3 Ex4 Chords Equidistant from Center

Lesson 3 Ex4 Chords Equidistant from Center are equidistant from P, so.

Lesson 3 Ex4 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.

A.A B.B C.C D.D Lesson 3 CYP4 A.12 B.36 C.72 D.32

A.A B.B C.C D.D Lesson 3 CYP4 A.12 B.36 C.72 D.32