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Today’s Lesson 8.G.5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle criterion for similarity of triangles. Goals By the end of the unit, I will…. » Be able to identify different types of angles and lines. » Use arguments to establish facts about angle sums and exterior angles of triangles. » Identify the angles created when parallel lines are cut by a transversal. » Create arguments for the similarity of triangles based on angles. Parallel Lines Lines in a plane that never intersect. Transversal A line that crosses two or more other lines. Complementary Angles Two angles that equal 90 degrees. Supplementary Angles Two angles that equal 180 degrees. x 150° These are supplementary angles. Supplementary angles add up to 180°. The supplementary angles add up to 180 degrees. x 150° 180 - 50 = x x = 30 30° Interior Angles Angles formed by a transversal and the lines it crosses, inside the parallel lines. Exterior Angles Angles formed by a transversal and the lines it crosses, outside the parallel lines. Alternate Angles Two angles formed by a transversal and the lines it crosses, on opposite sides of the transversal. Alternate angles have the same measurement. Corresponding Angles Two angles on the same side of the transversal, on a different line. Corresponding angles have the same measurement. 1 2 4 3 A B D C Corresponding Angles 1 2 4 3 A B D C Vertical Angles Two angles that share a vertex but not a side. Vertical angles have the same measurement. 43° x These angles are vertical. Vertical angles have the same angle measure. Lines a and b are parallel. c 110 a 4 5 b 8 2 3 6 7 If Angle 1 measures 110 degrees, what is the measure of Angle 3? 110° Lines a and b are parallel. c 110 a 4 5 b 8 2 3 6 7 If Angle 1 measures 110 degrees, what is the measure of Angle 4? 70° Lines a and b are parallel. c 110 a 4 5 b 8 2 3 6 7 If Angle 1 measures 110 degrees, what is the measure of Angle 8? 70° Lines a and b are parallel. c 110 a 4 5 b 8 2 3 6 7 If Angle 1 measures 110 degrees, what is the measure of Angle 7? 110° Lines a and b are parallel. c 1 a 4 5 b 8 2 3 52° 7 If Angle 6 measures 52 degrees, what is the measure of Angle 7? 128° Lines a and b are parallel. c 128° 1 a 4 52° b 128° 52° 5 8 2 3 52° 128° 52° 7 128° If Angle 6 measures 52 degrees, what is the measure of all the angles on the diagram?