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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.
Math Practice. 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?
3.3 Proofs with Parallel Lines EXPLORE IT Work with a partner. Write the converse of each conditional statement. Determine whether the converse is true. Justify your conclusion. a. Corresponding Angles Theorem If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 4 2 3 6 8 7 5 b. Alternate ...
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.
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.
9-1 PROVING LINES PARALLEL. You have already studied many situations involving intersecting lines that lie in the same plane. When all the points or lines in a set lie in a plane, we say that these points or these lines are coplanar.
1. If two lines are cut by a transversal so that alternate interior angles are (congruent, supplementary, complementary), then the lines are parallel. 2. If two lines are cut by a transversal so that same-side interior angles are (congruent, supplementary, complementary), then the lines are parallel. 3. If two lines are cut by a transversal so ...