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Name: Date: Page 1 of 2 Activity 3.2.2 Parallel Lines Corresponding Angles Converse 1. Prove the Parallel Lines Corresponding Angles Converse: If two lines are cut by a transversal and a pair of corresponding angles are congruent, then the lines are parallel. Fill in the blanks. Given: Transversal ⃡𝐸𝐹 intersects lines ⃡𝐴𝐵 and ⃡𝐶𝐷 at points E and F. m ∠ CFG = m ∠ AEF. Prove: ⃡𝐴𝐵 || ⃡𝐶𝐷 Proof: ⃡ and 𝐶𝐷 ⃡ either intersect or they are parallel. 𝐴𝐵 Why? __________________________ Suppose ⃡𝐴𝐵 and ⃡𝐶𝐷 intersect at a point we will call “H.” Then E, F, and H are the vertices of a triangle. In ∆EFH, ∠ HEF is an_____________ angle. (Note: ∠ HEF is another name for ∠ AEF) and ∠ HFG is an _________ angle. (Note: ∠ HFG is another name for ∠ CFG) We were given that m ∠ HEF = m _________________________. Why is this a problem? ________________________________________ What conclusion can you draw? _____________________________________ Activity 3.3.2 Connecticut Core Geometry Curriculum Version 3.0 Name: Date: Page 2 of 2 2. Prove: If two lines are perpendicular to the same line, then they are parallel. Complete this two-column proof. Given: ⃡𝐶𝐴 is perpendicular to ⃡𝐴𝐵 ⃡𝐷𝐵 is perpendicular to ⃡𝐴𝐵 Prove: ⃡𝐶𝐴 is parallel to ⃡𝐷𝐵 Proof: Statement Reason ⃡ is perpendicular to 𝐴𝐵 ⃡ 1. 𝐶𝐴 1. ___________________ 2. m ∠ CAE = 90° 2. ___________________ ⃡ ⃡ is perpendicular to 𝐴𝐵 3. 𝐷𝐵 3. ___________________ 4. m ∠ DBA = 90° 4. ___________________ 5. m ∠ CAE = m ∠ _________ 5. ___________________ 6. _______________________________ 6. ___________________ Activity 3.3.2 Connecticut Core Geometry Curriculum Version 3.0