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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.
Examples 1 and 2. You are asked to prove Theorem 3.10 in Exercise 30. GOAL 1 Prove that two lines are parallel. Use properties of parallel lines to solve real-life problems, such as proving that prehistoric mounds are parallel in Ex. 19. Properties of parallel lines help you predict the paths of boats sailing into the wind, as in Example 4. Why ...
Independent Practice: PROOFS OF PARALLEL LINES NAME: DATE: PERIOD: Geometry Unit 3 - Reasoning & Proofs w/Congruent Triangles Page 167 For # 1-3, given a ‖ b, state the postulate or theorem that justifies each conclusion. 1. 1 is supplementary to 8 because given _____ 2.
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.
Two lines that do not intersect are either parallel lines or skew lines. Two lines are parallel lines when they do not intersect and are coplanar. Two lines are skew lines when they do not intersect and are not coplanar. Also, two planes that do not intersect are parallel planes. Lines m and n are parallel lines (m n). Lines m and k are skew lines.
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 ...
parallel lines. Draw a transversal that intersects both parallel lines. a. Find the measures of the eight angles that are formed. What do you notice? b. Adjust the parallel lines and transversal so they intersect at different angles. Repeat part (a). How do your results compare to part (a)? c. Write conjectures about each pair of angles formed ...
