parallel lines proof day 4 · swbat: write proofs involving parallel and perpendicular lines , ∡...
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![Page 1: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/1.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
Parallel Lines Proof Day 4
![Page 2: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/2.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
,
Given
∡𝐁𝐀𝐂 ≅ ∡𝑩𝑪𝑨 ∡𝐁𝐃𝐄 ≅ ∡𝑩𝑨𝑪
𝑫𝑬 ∥ 𝑨𝑪 Converse of Corresponding ∡ Thrm
Transitive (1,2)
![Page 3: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/3.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
![Page 4: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/4.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
![Page 5: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/5.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
![Page 6: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/6.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
![Page 7: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/7.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
,
2
1 a
b
q
Given: Lines a and b cut by transversal q. ∡𝟏 ≅ ∡𝟐
Prove:
𝒂 ∥ 𝒃
![Page 8: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/8.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
,
Given:
∡𝟏 ≅ ∡𝟐
Prove:
𝒂 ∥ 𝒃
∡𝟏 ≅ ∡𝟐 3
∡𝟏 ≅ ∡𝟑
∡𝟐 ≅ ∡𝟑
𝒂 ∥ 𝒃
Given
Vertical ∡′𝒔 ≅
Transitive (1,2)
Converse of Corresponding ∡ Thrm
![Page 9: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/9.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
,
![Page 10: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/10.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
,
Given
𝑨𝑩 ≅ 𝑪𝑫
∡𝐁𝐃𝐂 ≅ ∡𝑫𝑩𝑨
𝑫𝑩 ≅ 𝑫𝑩 𝜟𝑨𝑫𝑩 ≅ 𝜟𝑪𝑫𝑩
𝑨𝑫 ≅ 𝑪𝑩
∡𝐀𝐃𝐁 ≅ ∡𝑪𝑩𝑫
𝑨𝑫 ∥ 𝑩𝑪
Given
AIA Thrm
Reflexive
SAS (2,3,4)
CPCTC
CPCTC
Conv. Of AIA Thrm
![Page 11: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/11.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
,
Given
∡𝟏 ≅ ∡𝑨
∡𝟐 ≅ ∡𝑩 AIA Thrm
∡𝐀 ≅ ∡𝑩 Transitive (2,3)
![Page 12: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/12.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
,
Given
∡𝐂 ≅ ∡𝑪𝑩𝑬
∡𝐀 ≅ ∡𝑬𝑩𝑫
∡𝑪𝑩𝑬 + ∡𝑬𝑩𝑫 = ∡𝑪𝑩𝑫
∡𝑨 + ∡𝑪 = ∡𝑪𝑩𝑫
AIA Theorem
Corresponding ∡ Thrm
Partition Postulate
Substitution (2,3)
![Page 13: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/13.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
,
![Page 14: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/14.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
,
![Page 15: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/15.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
,
![Page 16: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/16.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
Parallel Lines Proof Day 5
![Page 17: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/17.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
,
![Page 18: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/18.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
,
![Page 19: Parallel Lines Proof Day 4 · SWBAT: Write proofs involving Parallel and Perpendicular lines , ∡ Given ≅∡ ∡ ≅∡ ∥ Converse of Corresponding ∡ Thrm Transitive (1,2)](https://reader034.vdocuments.net/reader034/viewer/2022042710/5f60b84be51db4230831ff22/html5/thumbnails/19.jpg)
SWBAT: Write proofs involving Parallel and Perpendicular lines
,