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Name _______________________________________ Date __________________ Class __________________ Reteach Proving Lines Parallel If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel. Converse of the Corresponding Angles Postulate You can use the Converse of the Corresponding Angles Postulate to show that two lines are parallel. Given: 1 3 1 3 1 q || r Given: m 2 3 are corresponding angles. Converse of the Corresponding Angles Postulate 3x°, m 4 (x 50)°, x m 2 3(25)° m 4 (25 m 2 m 4 Transitive Property of Equality 4 Definition of congruent angles 2 75° 25 50)° Substitute 25 for x. 75° q || r Substitute 25 for x. Converse of the Corresponding Angles Postulate For Exercises 1 and 2, use the Converse of the Corresponding Angles Postulate and the given information to show that c || d. 1. Given: 2 2. Given: m 1 4 2x°, m 3 (3x 31)°, x 31 Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry Name _______________________________________ Date __________________ Class __________________ Reteach Proving Lines Parallel continued You can also prove that two lines are parallel by using the converse of any of the other theorems that you learned in Lesson 3-2. Theorem Hypothesis Converse of the Alternate Interior Angles Theorem Conclusion a || b 2 3 Converse of the Alternate Exterior Angles Theorem f || g 1 4 Converse of the Same-Side Interior Angles Theorem s || t m 1 m 2 180° For Exercises 3–5, use the theorems and the given information to show that j || k. 3. Given: 4 5 4. Given: m 3 12x°, m 5 5. Given: m 2 8x°, m 7 18x°, x (7x 6 9)°, x 9 Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry Name _______________________________________ Date __________________ Class __________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry