Parallel Lines and Transversals

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Presentation transcript:

Parallel Lines and Transversals Angles and Parallel Lines

Parallel Lines Parallel lines are coplanar lines that do not intersect

Skew Lines Skew lines are lines that do not intersect and are not coplanar.

Parallel Planes Parallel planes are planes that do not intersect.

Examples

Transversals A transversal is a line that intersects two or more coplanar lines at two different points.

Transversal Angle Pair Relationships

Corresponding Angles Postulate If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent

Parallel Lines and Angle Pairs

Examples If m∠2 = 4x + 7 and m∠7 = 5x – 13, find x

Perpendicular Transversal Theorem In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Examples Identify all planes parallel to plane DEH.

Examples Identify all segments parallel to plane AB.

Examples Identify all segments that intersect GH.

Examples Classify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. ∠4 and ∠5

Examples Classify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. ∠3 and ∠6

Examples Classify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. ∠7 and ∠11

Examples Indentify the transversal connecting each pair of angles. Then classify the relationship between each pair of angles. ∠2 and ∠12

Examples Indentify the transversal connecting each pair of angles. Then classify the relationship between each pair of angles. ∠13 and ∠10

Examples Indentify the transversal connecting each pair of angles. Then classify the relationship between each pair of angles. ∠6 and ∠14

Examples If m∠2 = 70, find the measure of each angle. ∠3

Examples If m∠2 = 70, find the measure of each angle. ∠1

Examples If m∠2 = 70, find the measure of each angle. ∠6

Examples Find the value of the variables in the figure.

Examples Find the value of the variables in the figure.

Examples Find the value of the variables in the figure.

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