Angles and parallel lines
3-2 Angles and Parallel Linesand the for season episode watch how i met your mother season 5 episode 10
Let's examine these pairs of angles in relation to parallel lines:. Alternate interior angles are " interior " between the parallel lines , and they " alternate " sides of the transversal. Notice that they are not adjacent angles next to one another sharing a vertex. When the lines are parallel, the alternate interior angles are equal in measure. Alternate exterior angles are " exterior " outside the parallel lines , and they " alternate " sides of the transversal. Notice that, like the alternate interior angles, these angles are not adjacent.
When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles. When the lines are parallel, the corresponding angles are congruent. When two lines are cut by a transversal, the pairs of angles on one side of the transversal and inside the two lines are called the consecutive interior angles. If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary. When two lines are cut by a transversal, the pairs of angles on either side of the transversal and inside the two lines are called the alternate interior angles.
Lines that are parallel , in the sense of Euclidean geometry geometry of the plane are lines in the same plane that never intersect. In coordinate geometry the algebra of lines , they are lines with the same slope. Parallel lines exist in the same plane but do not intersect. Parallel lines have the same slope. In diagrams, we usually indicate that two or more lines are parallel by placing an arrow symbol on each line, as shown.
Another word for opposite angles are vertical angles. Adjacent angles are angles that come out of the same vertex. Adjacent angles share a common ray and do not overlap. If we have two parallel lines and have a third line that crosses them as in the ficture below - the crossing line is called a transversal. The eight angles will together form four pairs of corresponding angles. Angles 1 and 5 constitutes one of the pairs. Corresponding angles are congruent.
Angles, parallel lines, & transversals