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3E Parallel Lines Name______________________________________ 1. How many lines can you construct through the given point parallel to the given line? 2. What about perpendicular to the given line? 3. Complete the information about the given diagram. Transversal: Interior Angles: Exterior Angles: Type of angles – List angle pairs in diagram Corresponding Angles: Alternate Interior Angles: Alternate Exterior Angles: Consecutive or Same-­‐Side Interior Angles: Consecutive or Same-­‐Side Exterior Angles: 4. What can you conclude about lines a and b? Angle measures relationship when parallel lines l and m are cut by a transversal 5. What can you conclude about lines m and n? 6. Use the diagram. If l∥m and ∠2 measures 65°, what is the measure of ∠6? 7-­‐9. Identify the theorem or postulate that is related to the measures of the angles in the pair given that l∥m, and find the unknown angle measures 7. Given: m∠4=150° and m∠6=(25x)° 8. Given: m∠3=(50x–50)° and m∠7=(20x+70)° 9. Given: m∠4=(60x+30)° and m∠5=(9x+12)° 10. If two parallel lines are cut by a transversal, alternate interior angles are congruent. Given: a∥b Prove: ∠2≅∠3 Jumbled Reasons Statements A. If two parallel lines are cut by a transversal, then corresponding angles are congruent. B. Adjacent angles that form a line are supplementary. C. Given D. Transitive Property of Congruence E. Vertical angles are congruent. F. Substitution Property 11. If two parallel lines are cut by a transversal, same-­‐side interior angles are supplementary. Reasons Given: a∥b Prove: ∠2 is supplementary to ∠3. Statements Reasons 12. In the diagram, lines j and k are parallel. ∠1 measures 30°. What is m∠6? 13. In the diagram, lines j and k are parallel. ∠4 measures 120°. What is m∠5? 14. In the diagram, which statement would allow the conclusion that j∥k? A. m∠2=m∠4 B. m∠2=m∠6 C. m∠4=m∠5 D. m∠1=m∠8 E. m∠2+m∠3=180 15. Which lines in the diagram must be parallel? I. !AB P HE II. !AC P HF 16. In the diagram, what are the values of x, m∠PQS, ∠SQR, and m∠SPQ? III. !AD P HG A. III only B. I and III C. II and III D. I, II, and III
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