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4 Given Vertical angles theorem Transitive property of congruence. Converse of the corresponding angles theorem. Alternate interior angles theorem Transitive property of congruence. Converse of alternate exterior angles theorem. If two lines are cut by a transversal such that corresponding angles are congruent, then the lines are parallel
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 you should learn it GOAL 2 GOAL 1 What you should learn 3.4 R E A L L I F E POSTULATE 16 ...
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.
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.
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 ...
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 ...
Proving Theorems about Parallel Lines Solving Real-Life Problems EXAMPLE 4 Proving the Alternate Exterior Angles Theorem Prove that if two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. SOLUTION Draw a diagram. Label a pair of alternate 1 3 2 p t q exterior angles as ∠1 and ∠2. You are ...
