Download Activity 3.3.3. Proving Lines are Parallel

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Activity 3.3.3. Proving Lines are Parallel
We have already proved (in activity 3.3.2) that if two lines cut by a transversal form congruent
corresponding angles, then the two lines are parallel. We will now use this fact to prove the
converses of two other theorems about parallel lines.
1. Parallel Lines Alternate Interior Angles Converse
Given: 𝑚∠2 = 𝑚∠3
Prove: 𝐴𝐵 ǁ 𝐷𝐶
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Activity 3.3.3
Connecticut Core Geometry Curriculum Version 3.0
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2. Parallel Lines Same Side Interior Angles Converse
Given: ∠2 and ∠5 are supplementary
Prove: 𝐴𝐵 ǁ 𝐷𝐶
Activity 3.3.3
Connecticut Core Geometry Curriculum Version 3.0
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3. Given: 𝑅𝑈 = 𝑅𝑄 and ∠𝑅𝑈𝑄 ≅ ∠𝑇𝑆𝑄
Prove: 𝑅𝑄 ǁ 𝑆𝑇
Activity 3.3.3
Connecticut Core Geometry Curriculum Version 3.0
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4. Given: 𝑉𝑌 = 𝑊𝑋 and 𝑉𝑊 = 𝑌𝑋
Prove: 𝑉𝑌 ǁ 𝑊𝑋
Activity 3.3.3
Connecticut Core Geometry Curriculum Version 3.0