![]() ![]() If two corresponding angles of a transversal across parallel lines are right angles, all angles are right angles, and the transversal is perpendicular to the parallel lines. Because of the vertical angles theorem, angle 4 and 8 and also measure 123°. What does that tell you about the lines cut by the transversal?Īnd now, the answers (try your best first!):Īngle 5 also measures 123°. You learn that corresponding angles are not congruent. ![]() Imagine a transversal cutting across two lines. If two corresponding angles of a transversal across parallel lines are right angles, what do you know about the figure?Ĭan you possibly draw parallel lines with a transversal that creates a pair of corresponding angles, each measuring 181°? You can use the Corresponding Angles Theorem even without a drawing. Looking at our BOLD MATH figure again, and thinking of the Corresponding Angles Theorem, if you know that angle 1 measures 123°, what other angle must have the same measure? If the lines cut by the transversal are not parallel, then the corresponding angles are not equal. Since the corresponding angles are shown to be congruent, you know that the two lines cut by the transversal are parallel. If you are given a figure similar to our figure below, but with only two angles labeled, can you determine anything by it? Converse of corresponding angles theorem The converse theorem allows you to evaluate a figure quickly. If a transversal cuts two lines and their corresponding angles are congruent, then the two lines are parallel. 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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