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Name: _______________________________ Notes 3.1 & 3.2 Parallel lines, angles, transversals 3.1 Pairs of Lines and Angles Term Parallel Lines Definition Two lines are parallel lines if they … Skew Lines Two lines are skew if they… Parallel Planes Two planes are parallel if they … Transversal A transversal is a line that… Perpendicular Lines Two lines that intersect… Parallel Postulate Diagram If there is a line and a point not on the line, then there is _______________________ line through the point parallel to the given line. There is exactly one line through P parallel to . Perpendicular Postulate If there is a line and a point not on that line, then there is _________________________ line through the point perpendicular to the given line. There is exactly one line through P perpendicular to . G13B Think of each segment in the diagram as part of a line. Complete the statement with parallel, skew, or perpendicular. WZ and ZR are__________WZ and ST are___________ QT and YS are__________ Plane WZR and plane SYZ are___________________________ Think of each segment in the diagram as part of a line. Which line(s) or plane(s) appear to fit the description? Line(s) parallel to EH Line(s) perpendicular to EH Line(s) skew to CD and containing point F Plane(s) perpendicular to plane AEH Plane(s) parallel to plane FGC Angles formed by a transversal (t) Two angles are ___________________________ angles if they have corresponding potions. For example ∠2 and ∠6 are above the lines and to the right of the transversal t. Two angles are ____________________________ angles if they line between the two lines and on opposite sides of the transversal. Two angles are _____________________________ angles if they line outside the two lines and on opposite sides of the transversal. Two angles are _______________________________ angles if they line between the two lines and on the same side of the transversal. Classify the angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles. List all possible correct answers. ∠2 and __?__ are corresponding angles. ∠4 and __?__ are consecutive interior angles. ∠l1 and __?__ are alternate interior angles. ∠12 and __?__ are alternate exterior angles. ∠l and ∠5 ∠11 and ∠16 ∠4 and ∠6 ∠16 and ∠10 ∠12 and ∠14 ∠7 and ∠13 3.2 Parallel lines and Transversals Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Alternate Interior Angle Theorem If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. Consecutive Interior Angle Theorem If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.