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Unit 4: Circles and Volume
Vocabulary Builder
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Daily Agenda Chord Bisect Radius Central Angle Diameter
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Daily Agenda Arc Diameter Radius Central Angle Bisect Chord
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Daily Agenda = 70 ×2= 35 ×2=
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Daily Agenda
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Daily Agenda
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Daily Agenda Semicircle Adjacent arcs Central angle diameter Major arc
Concentric circles Adjacent arcs Central angle diameter Major arc Minor arc circumference radius
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Daily Agenda
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Unit 4: Circles and Volume
4.1 Circle Vocabulary with Constructions
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Daily Agenda
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Daily Agenda
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Daily Agenda
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Daily Agenda
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Daily Agenda Tangent Chord Inscribed Angle Center Major Arc Tangent
Radius Central Angle
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Daily Agenda Minor Arc Diameter Point of Tangency Secant Semicircle
Central Angle Chord Inscribed Angle
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Daily Agenda Tangent to a Circle
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Daily Agenda Circumscribed Circle
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Construction: Inscribed Circle
Daily Agenda Construction: Inscribed Circle
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4.1 Construction of Circles
Daily Agenda 4.1 Construction of Circles
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4.1 Construction of Circles
Daily Agenda 4.1 Construction of Circles
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Unit 4: Circles and Volume
4.2 Circumference and Arc Length of a Circle
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Daily Agenda degrees radians 360˚ 2π
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Daily Agenda Converting between Degrees and Radians 𝝅 𝟗 𝟓𝝅 𝟔 𝝅 𝟒 𝟐𝟕𝟎°
𝟐𝟎× 𝝅 𝟏𝟖𝟎 = 𝟏𝟓𝟎× 𝝅 𝟏𝟖𝟎 = 𝝅 𝟗 𝟓𝝅 𝟔 𝟒𝟓× 𝝅 𝟏𝟖𝟎 = 𝝅 𝟒 𝟑𝝅 𝟐 × 𝟏𝟖𝟎 𝝅 = 𝟓𝝅 𝟑 × 𝟏𝟖𝟎 𝝅 = 𝟐𝟕𝟎° 𝟑𝟎𝟎° 𝝅 𝟏𝟐 × 𝟏𝟖𝟎 𝝅 = 𝟏𝟓°
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Daily Agenda 𝟏𝟔𝝅 𝟗 𝟏𝟏𝝅 𝟏𝟖 𝟕𝝅 𝟒 𝟐𝟖𝟖° 𝟐𝟏𝟎° 𝟖𝟏𝟎° 𝟑𝟐𝟎× 𝝅 𝟏𝟖𝟎 =
𝟏𝟏𝟎× 𝝅 𝟏𝟖𝟎 = 𝟑𝟏𝟓× 𝝅 𝟏𝟖𝟎 = 𝟏𝟏𝝅 𝟏𝟖 𝟕𝝅 𝟒 𝟖𝝅 𝟓 × 𝟏𝟖𝟎 𝝅 = 𝟕𝝅 𝟔 × 𝟏𝟖𝟎 𝝅 = 𝟗𝝅 𝟐 × 𝟏𝟖𝟎 𝝅 = 𝟐𝟖𝟖° 𝟐𝟏𝟎° 𝟖𝟏𝟎°
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Daily Agenda perimeter circumference diameter radius double ratio π
𝟐𝟐 𝟕 3.14
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Daily Agenda 𝟐𝝅 𝟏𝟐 = 𝟐𝝅 𝟗 = 𝟐𝟒𝝅 𝟏𝟖𝝅 𝟐𝝅 𝟐.𝟖 = 𝟐𝝅 𝟏𝟕.𝟓 = 5.6𝝅 𝟑𝟓𝝅
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Daily Agenda degrees Angle measure circumference Arc Length
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Daily Agenda 𝟕𝟕𝝅 𝟒 𝟏𝟑𝝅 𝟔 𝟑𝟗𝝅 𝟒 𝟗𝟓𝝅 𝟔 𝟐𝝅(𝟏𝟏)× 𝟑𝟏𝟓 𝟑𝟔𝟎 = 𝟏𝟑× 𝝅 𝟔 =
𝟐𝝅(𝟏𝟗)× 𝟏𝟓𝟎 𝟑𝟔𝟎 = 𝟏𝟑× 𝟑𝝅 𝟒 = 𝟗𝟓𝝅 𝟔 𝟑𝟗𝝅 𝟒
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4.2 Circumference and Arc Length
Daily Agenda 4.2 Circumference and Arc Length
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4.2 Circumference and Arc Length
Daily Agenda 4.2 Circumference and Arc Length
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Unit 4: Circles and Volume
4.3 Circumference and Arc Length of a Circle
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Daily Agenda area radius 𝝅 (𝟕) 𝟐 = 𝟒𝟗𝝅 𝝅 (𝟐𝟗) 𝟐 = 𝟖𝟒𝟏𝝅
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Daily Agenda 𝝅 (𝟏𝟕.𝟓) 𝟐 = 𝟑𝟎𝟔.𝟐𝟓𝝅 𝝅 (𝟏𝟐) 𝟐 = 𝟏𝟒𝟒𝝅
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Daily Agenda Area of a Sector area angle ratio
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Daily Agenda (𝟏𝟐𝟎)𝝅 (𝟗) 𝟐 𝟑𝟔𝟎 = (𝟕𝟎)𝝅 (𝟔) 𝟐 𝟑𝟔𝟎 = 𝟕𝝅 𝟐𝟕𝝅
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Daily Agenda (𝟏𝟓𝟎)𝝅 (𝟑) 𝟐 𝟑𝟔𝟎 = 𝟏 𝟐 𝟒 𝟐 𝟑𝝅 𝟐 = 𝟕𝝅 𝟏𝟐𝝅
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4.3 Area and Area of a Sector
Daily Agenda 4.3 Area and Area of a Sector
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4.3 Area and Area of a Sector
Daily Agenda 4.3 Area and Area of a Sector
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Unit 4: Circles and Volume
4.4 Central and Inscribed Angles
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Daily Agenda arc central 80˚ arc-like length central vertex measure
Intercepted arc
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Daily Agenda 72˚ 21˚ 108˚ 93˚ 267˚ 90˚ 124˚ 236˚ 304˚
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Daily Agenda 16 167˚ 13˚ 347˚ 21 167˚ 98˚ 262˚ 201˚
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Inscribed angle Daily Agenda Intercepted arc subtends
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Daily Agenda 31˚ 226˚ 176˚ 121˚
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right Daily Agenda 90˚ congruent mACD 41˚ 41˚ 90˚
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right Daily Agenda 90˚ congruent mACD 73˚ 54˚ 73˚
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Daily Agenda supplementary 𝒎∠𝑨+𝒎∠𝑪=𝟏𝟖𝟎 𝒎∠𝑩+𝒎∠𝑫=𝟏𝟖𝟎 72˚ 108˚ x = 3 87˚
96˚ x = 11 129˚ 84˚
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4.4 Central and Inscribed Angles
Daily Agenda 4.4 Central and Inscribed Angles
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4.4 Central and Inscribed Angles
Daily Agenda 4.4 Central and Inscribed Angles
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Unit 4: Circles and Volume
4.5 Congruent Chords and Arcs
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Daily Agenda circle radius chord diameter longest twice
equidistant radius chord diameter longest twice Their corresponding arcs are ≅ 𝐦 𝑨𝑩 =𝐦 𝑪𝑫 𝑨𝑩=𝑪𝑫 Their corresponding arcs are ≅ 𝑨𝑩=𝑪𝑫 𝑬𝑭=𝑬𝑮 perpendicular bisects chord arc 𝑬𝑯⊥𝑨𝑩 𝑨𝑭=𝑭𝑩 𝐦 𝑨𝑯 =𝐦 𝑯𝑩
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Daily Agenda 13 71˚ 10
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Daily Agenda 27 29 37
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Daily Agenda 9 18 9 42˚ 84˚
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Daily Agenda 34 17 52˚ 52˚ 26˚
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4.5 Congruent Chords and Arcs
Daily Agenda 4.5 Congruent Chords and Arcs
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4.5 Congruent Chords and Arcs
Daily Agenda 4.5 Congruent Chords and Arcs
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Unit 4: Circles and Volume
4.5 Congruent Chords and Arcs
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Daily Agenda 𝟏 𝟐 𝒎 𝑨𝑫 +𝒎 𝑩𝑪 𝟏 𝟐 𝒎 𝑨𝑫 +𝒎 𝑪𝑫 77˚ 50˚
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Daily Agenda 𝟏 𝟐 𝒎 𝑨𝑫 +𝒎 𝑩𝑪 𝟏 𝟐 𝒎 𝑨𝑫 +𝒎 𝑪𝑫 118˚ 183˚
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Daily Agenda 𝟏 𝟐 𝒎 𝑨𝑩 𝟏 𝟐 𝒎 𝑨𝑪𝑩 154˚ 58˚
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Daily Agenda 𝟏 𝟐 𝒎 𝑨𝑩 𝟏 𝟐 𝒎 𝑨𝑪𝑩 84˚ 104˚
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Daily Agenda 37˚ 74˚ 133˚ 𝟏 𝟐 𝒎 𝑩𝑫 −𝒎 𝑩𝑪 𝟏 𝟐 𝒎 𝑪𝑬 −𝒎 𝑩𝑫
𝟏 𝟐 𝒎 𝑪𝑬 −𝒎 𝑩𝑫 𝟏 𝟐 𝒎 𝑩𝑫 −𝒎 𝑩𝑪 𝟏 𝟐 𝒎 𝑩𝑫𝑪 −𝒎 𝑩𝑪 37˚ 74˚ 133˚
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Daily Agenda 𝟏 𝟐 𝒎 𝑪𝑬 −𝒎 𝑩𝑫 𝟏 𝟐 𝒎 𝑩𝑫 −𝒎 𝑩𝑪 𝟏 𝟐 𝒎 𝑩𝑫𝑪 −𝒎 𝑩𝑪 24˚ 48˚ 72˚
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Daily Agenda 𝒂∙𝒃=𝒄∙𝒅 𝒂(𝒂+𝒃)=𝒄(𝒄+𝒅) 𝒂 𝟐 =𝒃(𝒃+𝒄) 21 15 36
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Daily Agenda 𝒂∙𝒃=𝒄∙𝒅 𝒂 𝟐 =𝒃(𝒃+𝒄) 𝒂(𝒂+𝒃)=𝒄(𝒄+𝒅) 13 40 5
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one Daily Agenda perpendicular radius yes 20.2
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one Daily Agenda perpendicular radius no 14.2
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Daily Agenda 42.5 180
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Daily Agenda 29 73
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4.5 Congruent Chords and Arcs
Daily Agenda 4.5 Congruent Chords and Arcs
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4.5 Congruent Chords and Arcs
Daily Agenda 4.5 Congruent Chords and Arcs
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