Converse geometry xl12/9/2023 The converse of the Corresponding Angles Theorem is also interesting: They share a vertex and are opposite each other. The angles to either side of our 57° angle – the adjacent angles – are obtuse. If you have a two parallel lines cut by a transversal, and one angle ( angle 2) is labeled 57°, making it acute, our theorem tells us that there are three other acute angles are formed. Properties of lines known from corresponding angles theorem If one is a right angle, all are right anglesĪll eight angles can be classified as adjacent angles, vertical angles, and corresponding angles Corresponding angles theoremīecause of the Corresponding Angles Theorem, you already know several things about the eight angles created by the three lines: The Corresponding Angles Postulate is simple, but it packs a punch because, with it, you can establish relationships for all eight angles of the figure. If a transversal cuts two parallel lines, their corresponding angles are congruent. The Corresponding Angles Theorem says that: When a transversal line crosses two lines, eight angles are formed. Here are the four pairs of corresponding angles: Can you find all four corresponding pairs of angles? What are corresponding angles Which angles are corresponding angles?Ĭan you find the corresponding angle for angle 2 in our figure? Identifying corresponding angles exampleĭid you notice angle 6 corresponds to angle 2 ? They are a pair of corresponding angles. They do not touch, so they can never be consecutive interior angles. You can have alternate interior angles and alternate exterior angles.Ĭorresponding angles are never adjacent angles. Angles that are on the opposite side of the transversal are called alternate angles. Corresponding angles and transversal explainedĬorresponding angles are just one type of angle pair. One is an exterior angle (outside the parallel lines), and one is an interior angle (inside the parallel lines). Two angles correspond or relate to each other by being on the same side of the transversal.
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