3.3+Parallel+Lines+&+Transversals

Summary: This section will teach you how to prove and use results about parallel lines and transversals and use the properties of parallel lines to solve real life problems. It will include new theorems and postulates that have to do with parallel lines and transversal. You will learn new postulates and theorems to help you do more proofs of more difficulty.

Important Vocabulary:
 * Corresponding Angle Postulate:** If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent. If two lines in a plane are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
 * Alternate Interior Angle Theorem:** If two parallel lines are cut by a transversal, then each pair of alternate interior angles are congruent. If two lines in a plane are cut by a transversal so that a pair of alternate angles are congruent, then the lines are parallel.
 * Consecutive Interior Angle Theorem:** If two parallel lines are cut by a transversal, then each pair of consecutive interior angles are supplementary. If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles are supplementary, then the two lines are parallel.
 * Alternate Exterior Angle Theorem:** If two parallel lines are cut by a transversal, then each pair of alternate exterior angles are congruent. If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel.
 * Consecutive Exterior Angle Theorem:** If two parallel lines are cut by a transversal, then each pair of consecutive exterior angles are supplementary. If two lines in a plane are cut by a transversal so that a pair of consecutive exterior angles is supplementary, then the two lines are parallel.
 * Perpendicular Transversal Theorem:** In a plane, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other. In a plane, if two lines are perpendicular to the same line, then they are parallel.
 * Parallel Postulate:** If there is a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.

Practice Websites: http://www.mathwarehouse.com/geometry/angle/parallel-lines-transversal-practice.php http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_AnglesParallelLinesTransversals.xml

Extra Help:

1. The value of //y// is 25.

2. If angle 7 is 46º, what is the measure of angles 1, 2, 3, 4, 5, 6, and 8? State the reason for finding the measures of the 7 angles. Angle 1: 134º Angle 2: 46º Angle 3: 46º Angle 4: 134º Angle 5: 134º Angle 6: 46º Angle 8: 134º

3. prove the Alternate Interior Angle Theorem (page 144) 1. given- p//q 2. corresponding angle postulate- angle 1 is congruent to angle 2 3. vertical angle theorem angle 2 is congruent to angle 3 4. transitive property- angle 1 is congruent to angle 2


 * pictures taken from the online text book.*

More Practice:
 * the answers are written in red below the problem. (: enjoy!*