3.2 use parallel lines and transversals
- 1. 3.23.2 Use Parallel Lines and Transversals Bell Thinger ANSWER alternate interior 1. 5, 7 2. 3, 6 3. 1, 8 ANSWER alternate exterior ANSWER corresponding Identify the type of angles.
- 2. 3.2
- 3. 3.2Example 1 SOLUTION By the Corresponding Angles Postulate, m 5 = 120°. Using the Vertical Angles Congruence Theorem, m 4 = 120°. Because 4 and 8 are corresponding angles, by the Corresponding Angles Postulate, you know that m 8 = 120°. The measure of three of the numbered angles is 120°. Identify the angles. Explain your reasoning.
- 4. 3.2
- 5. 3.2Example 2 ALGEBRA Find the value of x. SOLUTION By the Vertical Angles Congruence Theorem, m 4 = 115°. Lines a and b are parallel, so you can use the theorems about parallel lines. Consecutive Interior Angles Theoremm 4 + (x+5)° = 180° Substitute 115° for m 4.115° + (x+5)°= 180° Combine like terms.x + 120 = 180 Subtract 120 from each side.x = 60
- 6. 3.2Guided Practice Use the diagram. 1. If m 1 = 105°, find m 4, m 5, and m 8. Tell which postulate or theorem you use in each case. Vertical Angles Congruence Theorem. Corresponding Angles Postulate.m 5 =105° Alternate Exterior Angles Theoremm 8 =105° m 4 = 105° ANSWER
- 7. 3.2 Use the diagram. If m 3 = 68° and m 8 = (2x + 4)°, what is the value of x? Show your steps. 2. Guided Practice m 3 = m 7 68 + 2x + 4 = 180 2x + 72 = 180 2x = 108 x = 54 m 7 + m 8 = 180 ANSWER
- 8. 3.2Example 3 Prove that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. SOLUTION Draw a diagram. Label a pair of alternate interior angles as 1 and 2. You are looking for an angle that is related to both 1 and 2. Notice that one angle is a vertical angle with 2 and a corresponding angle with 1. Label it 3. GIVEN : p q PROVE : 1 2
- 9. 3.2 GIVEN : p q PROVE : 1 2 STATEMENTS REASONS p q1. 1. Given 2. Corresponding Angles Postulate 3. Vertical Angles Congruence Theorem Transitive Property of Congruence 4. Example 3 2. 1 3 3. 3 2 4. 1 2
- 10. 3.2Example 4 When sunlight enters a drop of rain, different colors of light leave the drop at different angles. This process is what makes a rainbow. For violet light, m 2 = 40°. What is m 1? How do you know? Science SOLUTION Because the sun’s rays are parallel, 1 and 2 are alternate interior angles. By the Alternate Interior Angles Theorem, 1 2. By the definition of congruent angles, m 1 = m 2 = 40°.
- 11. 3.2Guided Practice 3. In the proof in Example 3, if you use the third statement before the second statement, could you still prove the theorem? Explain. Yes; 3 and 2 congruence is not dependent on the congruence of 1 and 3. SAMPLE ANSWER
- 12. 3.2 Suppose the diagram in Example 4 shows yellow light leaving a drop of rain. Yellow light leaves the drop at an angle of 41°. What is m 1 in this case? How do you know? 4. WHAT IF? Guided Practice 41°; 1 and 2 are alternate interior angles. By the Alternate Interior Angles Theorem, 1 2. By the definition of congruent angles, m 1 = m 2 = 41°. ANSWER
- 13. 3.2Exit Slip What theorem justifies each statement? 2. 4 and 6 are supplementary. 3. If m 2 = 115 , find m 7. o 115ANSWER o Alt. Interior Thm.s ANSWER Consec. Interior Thm. s ANSWER 1. 3 6
- 14. 3.2 4. Find the values of x and y. 17.5, 35ANSWER Exit Slip
- 15. 3.2 82ANSWER o 5. The figure shows a plant trellis . If m 1 = 82 o , find m 2. Exit Slip
- 16. 3.2 6. If m 1 = 105 o , find all other angle measures.
- 17. 3.2 Homework Pg 161-164 #22, 23, 24, 31, 41