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Math 20-2 Geometry: Lesson #1 Transversals Objective: By the end of this lesson, you should be able to: - Generalize, using inductive reasoning, the relationships between pairs of angles formed by transversals and parallel lines. - Determine the measures of angles in a diagram that includes parallel lines, angles and triangles, and justify the reasoning. - Determine if lines are parallel, given the measure of an angle at each intersection formed by the lines and a transversal. E A s t u v B C w x y z D F Vocabulary Transversal – Interior angles – Exterior angles – Opposite angles – Corresponding angles – Math 20-2 Geometry: Lesson #1 Alternate interior angles – Alternate exterior angles – Key Point: There are relationships between the angles formed by parallel lines and a transversal. e.g. 1) Use a ruler to draw a transversal across the two parallel lines shown. (Make sure it is not perpendicular to the lines.) Then use a protractor to measure all eight angles formed. Make a conjecture about the following sets of angles formed by parallel lines and a transversal: Corresponding angles: Alternate interior angles: Alternate exterior angles: Interior angles on the same side of the transversal: Exterior angles on the same side of the transversal: Math 20-2 Geometry: Lesson #1 e.g. 2) The horizontal lines are parallel. Determine the measure of every indicated angle. Give reasons for your statements. b c a 112 d e 53 e.g. 3) Are the lines shown parallel? Justify your answer. 158 23 e.g. 5) Solve for x in each of the diagrams below: a) 3x 17 107 2x Math 20-2 Geometry: Lesson #1 b) x 6 5 x Assignment: p. 72 #2, 5 p. 79-82 #4, 20