Angles and Transversals of Parallel Lines
MAYRA RUIZ
Created on September 17, 2023
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Transcript
Angles and Transversals of Parallel Lines
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Definitions:
Parallel Lines: Two lines that never intersect. Transversal: A line that intersects two or more lines.When parallel lines are intersected by a transversal, many angles are formed. They will form special relationships between pairs
Supplementary angles are two angles that add up to 180˚. They make a straight line.
Parallel Lines
Transveral Lines
Supplementary Angles: Supplementary angles are two angles that add up to 180 degrees. In other words, if you have two angles, and the sum of their measures is 180 degrees, those angles are considered supplementary to each other.
Definition of Supplementary Angles: As mentioned, supplementary angles are pairs of angles whose measures sum up to 180 degrees. Mathematically, if you have two angles, A and B, that are supplementary, you can express it as: A + B = 180° Rearranging the Equation: To isolate the measure of angle A, you can rearrange the equation like this: A = 180° - B
If you know the measure of one angle, you can always find the measure of its supplementary angle by subtracting it from 180 degrees. So if the measure of one angle is 'x' degrees, the measure of its supplementary angle is '180 – x' degrees.
Corresponding angles of parallel lines crossed by transversals are congruent because of the unique geometric relationships that exist in such configurations. To understand why corresponding angles are congruent, it's essential to grasp the properties of parallel lines and transversals.
Definition of Corresponding Angles: Corresponding angles are pairs of angles that occupy the same relative positions at each intersection point along the transversal. In other words, they are formed by the same pairs of intersecting lines on each side of the transversal. Alternate Interior Angles Theorem: When you have a pair of parallel lines crossed by a transversal, one important geometric relationship is that the alternate interior angles are congruent. This means that if you have two parallel lines and a transversal cutting through them, the angles on the inside, on opposite sides of the transversal, will be equal in measure.