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Regents Geometry Chapter 3 Study Guide Use the following website for on-line resources (practice tests and quizzes): http://www.glencoe.com/sec/math/geometry/geo/geo_04/ Select what you want to do and then go to Chapter 3 Parallel and Perpendicular Lines. Chapter 3 – Parallel and Perpendicular Lines Definitions with images can be found using Quizlet: http://quizlet.com/24451796/familiarize/ Parallel Lines Skew Lines Parallel Planes Transversal Interior Angles Exterior Angles Lines in the same plane that never intersect. Lines that do not intersect and are not in the same plane. Planes that never intersect. A line that intersects two or more lines in a plane at different points Angles that lie inside parallel lines. Angles that lie outside parallel lines. Consecutive Interior Angles Alternate Interior Angles Alternate Exterior Angles Corresponding Angles Angles that are on the same side of the transversal and inside the parallel lines. Angles that are on opposite sides of the transversal and inside the parallel lines. Angles that are on opposite sides of the transversal and outside the parallel lines. Angles that are in the same position on the parallel lines with respect to the transversal. Corresponding Angles Postulate If two parallel lines are cut by a transversal, than each pair of corresponding angles is congruent. Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent. Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary (add to 180°). Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent. Slope of a Line Definition The ratio of the change along the y-axis to the change along the x-axis. Commonly referred to as "rise over run". Slope of a Line Equation 𝒎 = 𝒙𝟐 −𝒙𝟏 Slope of a Vertical Line Is undefined because the denominator of the slope formula (𝑥2 − 𝑥1 ) is equal to zero. 𝒚 −𝒚 𝟐 𝟏 Slope of a Horizontal Line A Line with Positive Slope A Line with Negative Slope Is equal to zero because the numerator of the slope formula (𝑦2 − 𝑦1 ) is equal to zero. Rises from left to right. Falls from left to right. Postulate: Slopes of Parallel Lines Two non-vertical lines have the same slope if and only if they are parallel. (𝑚1 = 𝑚2 ) Note: All vertical lines are parallel. Postulate: Slopes of Perpendicular Lines Two non-vertical lines are perpendicular if and only if the product of their slopes is equal to −1. 1 (𝑚1 𝑚2 = −1 or 𝑚1 = − 𝑚 ) 2 Note: Vertical lines are perpendicular to horizontal lines. Slope-Intercept Form of the Equation of a Line 𝑦 = 𝑚𝑥 + 𝑏 Point-Slope Form of the Equation of a Line 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 ) 𝒚-intercept The point where a line (or curve) intersects the 𝑦-axis. Equation of a Horizontal Line 𝑦 = 𝑏 (Note: 𝑥-values change, 𝑦-value is constant.) Equation of a Vertical Line 𝑥 = 𝑎 (Note: 𝑦-values change, 𝑥-value is constant.) Postulate: Converse of Corresponding Angles If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. Postulate: Converse of Alternate Exterior Angles If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel. Postulate: Converse of Alternate Interior Angles If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. Postulate: Converse of Consecutive Interior Angles If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.