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Advanced Geometry Parallel and Perpendicular Lines Lesson 1 Parallel Lines Lines (segments & rays, also) are either parallel, l m intersecting, or skew. Skew Lines do not intersect are not coplanar AB and CD are skew. Planes can be parallel OR intersecting. Example: Name all segments that are parallel toAF . DE , BG, CH Name all segments that intersectGH . BG, FG, CH , EH Name all segments that are skew to FG . AD, DE , BC , CH , and CE Name all planes that are parallel to plane DEF. Figure from p. 143. Transversal Identify the pairs of lines to which each given line is a transversal. m l and n; l and p; n and p p l and m; l and n; m and n Whenever there are two lines and a transversal, eight angles are formed. t a b interior angles – angles between the two lines ∠3, ∠4, ∠5, ∠6 exterior angles – angles outside the two lines ∠1, ∠2, ∠7, ∠8 Alternate Interior Angles AIA ∠3 and ∠6 ∠4 and ∠5 •both angles are interior t •different sides of the transversal Alternate Exterior Angles AEA a b •both angles are exterior •different sides of the transversal ∠1 and ∠8 ∠2 and ∠7 Consecutive Interior Angles CIA ∠3 and ∠5 ∠4 and ∠6 •both angles are interior t •same side of the transversal Corresponding Angles • one interior angle and one exterior angle •same side of the transversal a b ∠1 and ∠5 ∠2 and ∠6 ∠3 and ∠7 ∠4 and ∠8 Identify each pair of angles and AIA, AEA, CIA, corresponding angles, vertical angles, or a linear pair. ∠5 and ∠12 AEA ∠10 and ∠3 corresponding angles ∠4 and ∠7 vertical angles ∠10 and ∠11 CIA ∠2 and ∠12 linear pair ∠3 and ∠14 AIA Name the transversal that forms each pair of angles. Then identify the pair of angles. ∠8 and ∠6 a corresponding angles ∠10 and ∠14 b AIA ∠2 and ∠16 c AEA ∠10 and ∠11 b CIA When the lines cut by a transversal are parallel, the four angle pairs have a special relationship. • AIA are congruent. Reminder: • AEA are congruent. • CIA are supplementary. • Vertical angles are ALWAYS congruent. • Corresponding angles are congruent. • Linear pairs are ALWAYS supplementary. In the figure a || b and m∠4 = 51. Find the measures of all numbered angles. Justify each answer. a b Find the measure of each angle if m∠1 = 62 and m∠7 = 107. What is the measure of ∠RTV? If m∠2 = 4x + 7 and m∠3 = 5x – 13, find m∠3. If m∠5 = 2x – 10, m∠6 = 4(y – 25), and m∠7 = x + 15. find x and y.