Download Two lines are parallel lines if they and more Summaries Analytical Geometry and Calculus in PDF only on Docsity!
Parallel Lines Two lines are parallel lines if they are coplanar and do not intersect. Skew Lines Lines that are not coplanar and do not intersect are called skew lines. Parallel Planes Two planes that do not intersect are called parallel planes.
The symbol || is read as “is parallel to.” Parallel Postulate If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line. Perpendicular Postulate If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.
Transversal A transversal is a line that intersects two or more coplanar lines at different points. Corresponding Angles Two angles are corresponding angles if they occupy corresponding angles. Alternate Exterior Angles Two angles are alternate exterior angles if they lie outside the two lines on opposite sides of the transversal. Alternate Interior Angles Two angles are alternate interior angles if they lie between the two lines on opposite sides of the transversal. Consecutive Interior Angles Two angles are consecutive interior angles if they lie between the two lines on the same side of the transversal. Consecutive interior angles are sometimes called same side interior angles. Perpendicular Line Theorems If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. If two sides of two adjacent angles are perpendicular, then the angles are complementary. If two lines are perpendicular, then they intersect to form four right angles.
Transversal Theorems: If two lines are cut by a transversal so that consecutive interior angles are supplementary, then…? If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel. Transversal Theorems: If two lines are cut by a transversal so that alternate exterior angles are congruent, then…? If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel. Parallel and Perpendicular Line Theorems If two lines are parallel to the same line, then they are parallel to each other. In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. The Slope of a Line Slope = Rise/Run m= (y 2 -y 1 )/(x 2 -x 1 ) In a coordinate plane, two nonvertical lines are parallel if and only if…? In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope. Any two vertical lines are…? Any two vertical lines are parallel.
The Slope Intercept Form of a Line Equation y = mx + b, where m is the slope and b is the y-intercept value. Lattice Points Points where grid lines cross are called lattice points. In a coordinate plane, two nonvertical lines are perpendicular if and only if…? In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is –1. Vertical and horizontal lines are…? Vertical and horizontal lines are perpendicular. Parallel Lines Two lines are parallel lines if they are coplanar and do not intersect. Skew Lines Lines that are not coplanar and do not intersect are called skew lines.
Alternate Exterior Angles Two angles are alternate exterior angles if they lie outside the two lines on opposite sides of the transversal. Alternate Interior Angles Two angles are alternate interior angles if they lie between the two lines on opposite sides of the transversal. Consecutive Interior Angles Two angles are consecutive interior angles if they lie between the two lines on the same side of the transversal. Consecutive interior angles are sometimes called same side interior angles. Perpendicular Line Theorems If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. If two sides of two adjacent angles are perpendicular, then the angles are complementary. If two lines are perpendicular, then they intersect to form four right angles. Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
Parallel Line Theorems: If two parallel lines are cut by a transversal then…? If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent, the pairs of consecutive interior angles are supplementary, and the pairs of alternate exterior angles are congruent. Parallel Line Theorems: If a transversal is perpendicular to one of two parallel lines then… If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
