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Proving Lines Parallel
November 26, 2013
SWBAT: Write proofs involving Parallel and Perpendicular lines
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SWBAT: Write proofs involving Parallel and Perpendicular lines
,
SWBAT: Write proofs involving Parallel and Perpendicular lines
,
X
𝑨𝑩 ∥ 𝑫𝑪, 𝑨𝑩 ≅ 𝑪𝑫 Given || AIA’s ∡𝑪𝑫𝑩 ≅ ∡𝑨𝑩𝑫 (A)
(S)
𝑫𝑩 ≅ 𝑫𝑩 Reflexive Prop. (S) 𝜟𝑪𝑫𝑩 ≅ 𝜟𝑨𝑩𝑫
∡𝐀𝐃𝐁 ≅ ∡CBD
SAS (1,2,3)
CPCTC AIA’s ≅ → ∥
𝑨𝑫 ≅ 𝑪𝑩 CPCTC
SWBAT: Write proofs involving Parallel and Perpendicular lines
,
𝑫𝑪𝑬 ∥ 𝑨𝑩 , ∡𝟏 ≅ ∡𝟐 Given || AIA’s ∡𝟏 ≅ ∡𝑨, ∡𝟐 ≅ ∡𝑩
∡𝑨 ≅ ∡𝑩 Transitive Prop. (1, 2)
SWBAT: Write proofs involving Parallel and Perpendicular lines
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𝑩𝑬 ∥ 𝑨𝑪 Given || CA’s = 𝒎∡𝑨 = 𝐦∡𝑬𝑩𝑫
𝒎∡𝑪𝑩𝑫 = 𝒎∡𝑬𝑩𝑫 + 𝐦∡𝑪𝑩𝑬
𝒎∡𝑪 = 𝐦∡𝑪𝑩𝑬 || AIA’s =
Partition Postulate 𝒎∡𝑪𝑩𝑫 = 𝒎∡𝑨 + 𝐦∡𝑪 Substitution Prop (2&3 into 4)
SWBAT: Write proofs involving Parallel and Perpendicular lines
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E midpoint of 𝐵𝐶 𝑎𝑛𝑑 𝐷𝐹 Given 𝑩𝑬 ≅ 𝑪𝑬, 𝑫𝑬 ≅ 𝑭𝑬 midpoint 2 ≅ segs (S) (S)
∡BED ∡ CEF Vertical ∡s (A)
BED CEF SAS (2,3,2)
∡𝐀𝐁𝐄 ≅ ∡FCE CPCTC
AIA’s ≅ → ∥
SWBAT: Write proofs involving Parallel and Perpendicular lines
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