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  1. Analyze Relationships. What is the sum of the measures of a pair of consecutive interior angles? Does it stay the same or change when you adjust the lines? intersects both parallel lines. Find the measures of the eight angles that are formed. What do you notice? Adjust the parallel lines and transversal so they intersect at different angles.

  2. Essential Question. For which of the theorems involving parallel lines and transversals is the converse true? Exploring Converses. Work with a partner. Write the converse of each conditional statement. Draw a diagram to represent the converse. Determine whether the converse is true. Justify your conclusion.

  3. Here are some examples of pairs of lines in a coordinate plane. a. 2 x + y = 2 These lines are not parallel b. 2 x + y = 2 These lines are coincident x − y = 4 or perpendicular.

  4. Utilizing Parallel Lines in Proofs Reasons 1) Given 2) Given 3) If parallel lines cut by transversal, then altemate angles are conguent 4) Transitive property 5) If base angles are congruent, then triangle is isosceles AEK BED 1) 2) 5) ABE is isosceles BED EBA BAE BAE or Recognizing the altemate interior angles... Example: Given: Prove: Circle E

  5. What you should learn. GOAL 1. Prove that two lines are parallel. re parallel. You can use the following postulate and theorems to p. GOAL 2 Use properties of lines are parallel. parallel lines to solve real-life problems, such as proving that prehistoric mounds are parallel in Ex. 19. Why you should learn it. n Exa.

  6. Work with a partner. Write the converse of each conditional statement. Determine whether the converse is true. Justify your conclusion. Corresponding Angles Theorem. If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. b. Alternate Altern Interior Angles Theorem.

  7. 5.5 Parallel Lines and Transversals How can you use properties of parallel lines to solve real-life problems? Work with a partner. Talk about what it means for two lines to be parallel. Decide on a strategy for drawing two parallel lines. Use your strategy to carefully draw two lines that are parallel. Now, draw a third line

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