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Angles Created When Parallel Lines are Cut by a Transversal

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Basics on the topic Angles Created When Parallel Lines are Cut by a Transversal

Learn about the angle relationships created when two parallel lines are cut by a transversal.

Transcript Angles Created When Parallel Lines are Cut by a Transversal

Angles created when parallel lines are cut by a transversal. These lines here are parallel and will never cross. A line that cuts through parallel lines is called a transversal. This grouping of lines has created eight angles which we can label with variables until we know the measurements. Each angle is related to another, some are congruent and some are supplementary. Remember, congruent means that the angles have the same measurement, so they are equal. Supplementary angles are two angles that have a sum of one hundred eighty degrees. These pairs can be any two angles directly next to one another since they are on a straight line which is one hundred eighty degrees. Angles g and h are supplementary, as well as e and f, and many other pairs. But, supplementary angles don't need to be next to each other. Any pair of angles that has a sum of one hundred eighty degrees is considered supplementary. For example, angles a and f are considered supplementary, because the angles have a sum of one hundred eighty. Vertical angles are a pair of angles opposite from one another, and they are congruent. Here, we have four pairs of vertical angles, a and c, b and d, e and g, and also f and h. Alternate exterior angles are a pair of angles on the outside of the parallel lines but are on opposite sides. These angle pairs are also congruent. A and g are an alternate exterior angle pair, as well as b and h. Alternate interior angles are a pair of angles on the inside of the parallel lines but on opposite sides of the transversal. The angle pairs of c and e, and d and f are congruent because they are alternate interior angles. Corresponding angles refer to angles that are in the same position but on a different parallel line of the two. These angles are congruent, and some of the pairs include b and f, or d and h, amongst other pairs. Let's practice applying what we learned by looking at this map that contains two parallel roads cut by a transversal road. What angle is d paired with to create vertical angles? Angle b is vertical with angle d and they are congruent. Name the angle that is an alternate exterior angle pair with angle x. Angle c and x are alternate exterior angles and therefore are congruent. What angle is corresponding with angle y? Angle b is because it is in the same position, therefore it is congruent. If angle w had a measurement of seventy degrees, what would be the measurement of angle y? Since this pair is vertical, they would both be seventy degrees. Once we know just one of these angles, we can actually find all of the remaining angles. If angle y is seventy degrees, then so is b since they are corresponding, and therefore d is as well since it is y's alternate exterior angle. The remaining angles must be supplementary with seventy degrees, and in order to find that we can subtract seventy from one hundred eighty to get one hundred ten. Let's summarize what we have learned. Two parallel lines cut by a transversal create eight angles, all of which are related to each other. Angles that are congruent have the same measurement, and angles that are supplementary add to one hundred eighty degrees. Understanding angle measurements and relationships is important when it comes to maps, architecture, and engineering.