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Name ________________________________________ Date___________________ Class-CCGPS Geometry The angles in this figure can be compared using the following rules: Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Name the pairs of angles congruent by the Corresponding Angles Postulate. 1. ___________________________ 2. ___________________________ 3. ___________________________ 4. ___________________________ Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then the two pairs of alternate interior angles are congruent. Name the pairs of angles congruent by the Alternate Interior Angles Theorem. 5. ___________________________ 6. ___________________________ Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then the two pairs of alternate exterior angles are congruent. Name the pairs of angles congruent by the Alternate Exterior Angles Theorem. 7. ___________________________ 8. ___________________________ Same-Side Interior Angles Theorem If two parallel lines are cut by a transversal, then the two pairs of same-side interior angles are supplementary. Name the pairs of angles supplementary by the Same-Side Interior Angles Theorem. 9. ___________________________ 10. ___________________________ 11. If m247, then what is m6? How do you know? _______________________________________________________________________________________ 12. Based on the value for m6 from Exercise 11, what is m3? How do you know? _______________________________________________________________________________________ 13. The Corresponding Angles Postulate states that if two parallel lines are cut by a transversal, then the pairs of corresponding angles are _______________. 14. _______________ Congruent angles have _____________________ measures. Find each angle measure. 15. m1 _______________________ Find x. 17. 16. m2 _______________________ 18. ________________________________________ ________________________________________ Fill in the blanks to complete these theorems about angle pairs. 7. If two _____________________ lines are cut by a _____________________, then the two pairs of alternate interior angles are congruent. 8. If two parallel lines are cut by a transversal, then the two pairs of same-side interior angles are _____________________. 9. If two parallel lines are cut by a transversal, then the two pairs of alternate exterior angles are _____________________. Give two examples of each kind of angle pair in the figure. 10. alternate interior angles 11.alternate exterior angles 12.same-side interior angles _____________________ _____________________ _____________________ Complete the two-column proof to show that same-side exterior angles are supplementary. 5. Given: p || q Prove: m1 m3 180 Proof: Statements Reasons 1. p || q 1. Given 2. a. _______________________ 2. Lin. Pair Thm. 3. 1 2 3. b. _______________________ 4. c. _______________________ 4. Def. of s 5. d. _______________________ 5. e. _______________________
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