new angle relationships in circles day 5 · 2013. 2. 21. · swbat: identify the different angle...
TRANSCRIPT
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SWBAT: Identify the different Angle Relationships in Circles.
Angle Relationships in circles
Day 5
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SWBAT: Identify the different Angle Relationships in Circles.
Warm Up: (page 40)
3y + 4y + 8y = 360
15y = 360
y = 24
𝟐∡ = 𝑩𝑪 𝟐𝒙 = 4(24) 𝟐𝒙 = 96
𝒙 = 48
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SWBAT: Identify the different Angle Relationships in Circles.
Warm Up: (page 40)
132 + 82 = 214 𝟐 · ∡ = 𝑨𝑹𝑪
𝟐 · ∡ = 𝟐𝟏𝟒
∡ = 107˚
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SWBAT: Identify the different Angle Relationships in Circles. (page 41)
Outside the Circle
On the Circle
Inside the Circle
Tangent- Tangent ∡
Two Chords (Central ∡)
Chord –Tangent ∡
𝟐 ∙ 𝒎∡𝒙 = 𝒇 − 𝒏
𝟐 ∙ 𝒎∡𝒙 = 𝒏
𝒎∡𝒙 = 𝒏
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SWBAT: Identify the different Angle Relationships in Circles. (page 41)
Outside the Circle
Outside the Circle
On the Circle
Inside the Circle
Secant- Secant ∡
Chord –
Chord ∡
Inscribed ∡
Tangent- Secant ∡
𝟐 ∙ 𝒎∡𝒙 = 𝒇 − 𝒏
𝟐 ∙ 𝒎∡𝒙 = 𝒇 − 𝒏
𝟐 ∙ 𝒎∡𝒙 = 𝒇 + 𝒏
𝟐 ∙ 𝒎∡𝒙 = 𝒏
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SWBAT: Identify the different Angle Relationships in Circles. Example 1: (page 42)
ON
𝟐∡ = 𝒂𝒓𝒄
𝟐(𝟏𝟏𝟔˚) = 𝒏
𝟐𝟑𝟐˚ = 𝒏
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SWBAT: Identify the different Angle Relationships in Circles. Example 2: (page 42)
INSIDE
𝟐 ∙ ∡ = 𝒇 + 𝒏
y˚ 𝟐 ∙ 𝒎∡𝒚 = 𝟐𝟖 + 𝟐𝟎
𝟐 ∙ 𝒎∡𝒚 = 𝟒𝟖
𝒎∡𝒚 = 𝟐𝟒˚
m∡𝒙 =180-24 = 156˚
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SWBAT: Identify the different Angle Relationships in Circles. Example 3: (page 42)
OUTSIDE
𝟐 ∙ ∡ = 𝒇 − 𝒏 250°
𝟐 ∙ 𝒎∡𝒌 = 𝟐𝟓𝟎 − 𝟏𝟏𝟎
𝟐 ∙ 𝒎∡𝒌 = 𝟏𝟒𝟎
𝒎∡𝒌 = 𝟕𝟎°
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SWBAT: Identify the different Angle Relationships in Circles. Example 4: (page 43)
𝒎∡𝒌+𝒎𝑳𝑱 = 𝟏𝟖𝟎
𝟑𝟒° +𝒎𝑳𝑱 = 𝟏𝟖𝟎°
𝒎𝑳𝑱 = 𝟏𝟒𝟔°
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SWBAT: Identify the different Angle Relationships in Circles. Example 5: (page 43)
OUTSIDE
𝟐 ∙ ∡ = 𝒇 − 𝒏
𝟐 ∙ 𝒙 = 𝟕𝟓 − 𝟐𝟗
𝟐𝒙 = 𝟒𝟔
𝒙 = 𝟐𝟑°
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SWBAT: Identify the different Angle Relationships in Circles. Example 6: (page 43)
OUTSIDE
𝟐 ∙ ∡ = 𝒇 − 𝒏
𝟐 ∙ 𝒙 = 𝟏𝟒𝟎 − 𝟕𝟒
𝟐𝒙 = 𝟔𝟔
𝒙 = 𝟑𝟑°
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SWBAT: Identify the different Angle Relationships in Circles. Key Questions: (page 44)
𝟐𝒙 = 𝟕𝟎 𝒙 = 𝟑𝟓°
𝟐(𝟓𝟎°) = 𝒙
𝟏𝟎𝟎° = 𝒙
𝟐∡ = 𝒂𝒓𝒄 𝟐∡ = 𝒂𝒓𝒄
𝟐 ∙ ∡ = 𝒇 − 𝒏
𝟐 ∙ 𝒙 = 𝟗𝟎 − 𝟕𝟎 𝟐𝒙 = 𝟐𝟎
𝒙 = 𝟏𝟎° 𝟐 ∙ ∡ = 𝒇 − 𝒏
𝟐 ∙ 𝟒𝟎 = 𝒙 − 𝟐𝟓
𝟖𝟎 = 𝒙 − 𝟐𝟓
𝟏𝟎𝟓° = 𝒙
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SWBAT: Identify the different Angle Relationships in Circles. Key Questions: (page 44)
𝟖𝟎° + 𝒙° = 𝟏𝟖𝟎
𝒙° = 𝟏𝟎𝟎°
𝟐 ∙ 𝒙 = (𝟏𝟎𝟎 + 𝟖𝟎)
𝒙 = 𝟗𝟎°
𝟐𝒙 = 𝟏𝟖𝟎
𝟐 ∙ 𝟏𝟎𝟓 = (𝟏𝟎𝟎 + 𝒙)
𝟐𝟏𝟎 = 𝟏𝟎𝟎 + 𝒙
𝟏𝟏𝟎 = 𝒙
𝟐 ∙ ∡ = 𝒇 − 𝒏
𝟐 ∙ 𝒙 = 𝟏𝟏𝟎 − 𝟕𝟎
𝟐𝒙 = 𝟒𝟎
𝒙 = 𝟐𝟎°
𝟕𝟎
𝟐 ∙ ∡ = 𝒇 + 𝒏
𝟐 ∙ ∡ = 𝒇 + 𝒏
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SWBAT: Identify the different Angle Relationships in Circles.
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SWBAT: Identify the different Angle Relationships in Circles.
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SWBAT: Identify the different Angle Relationships in Circles.
𝟐 ∙ 𝒙 = (𝟖𝟕 + 𝟑𝟓)
𝒎∡𝒙 = 𝟔𝟏°
𝟐𝒙 = 𝟏𝟐𝟐
𝟐 ∙ ∡ = 𝒇 + 𝒏
𝒙
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SWBAT: Identify the different Angle Relationships in Circles.
𝟏𝟒𝟎 𝟒𝟎 𝒙
𝟐 ∙ ∡ = 𝒇 − 𝒏
𝟐 ∙ 𝟒𝟎 = 𝟏𝟒𝟎 − 𝒙
𝟖𝟎 = 𝟏𝟒𝟎 − 𝒙 𝒙 = 𝟔𝟎°
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SWBAT: Identify the different Angle Relationships in Circles.
𝟏𝟏𝟎 𝒙 𝟐 ∙ ∡ = 𝒇 − 𝒏
𝟐 ∙ 𝒙 = 𝟐𝟓𝟎 − 𝟏𝟏𝟎
𝟐𝒙 = 𝟏𝟒𝟎
𝒙 = 𝟕𝟎°