Download 3.1 Identify Pairs of Lines and Angles

Geometry Chapter 3: Parallel and Perpendicular Lines 3.1-­‐ Identify Pairs of Lines and Angles SWBAT: identify angle pairs formed by three intersecting lines. Common Core: G.CO.9
“Do Now” !
!"
a) Simplify: ! ÷ ! b) Find the slope between the points −3, 7 𝑎𝑛𝑑 (2, −4) Vocabulary: Ø Parallel lines-­‐ Two lines are parallel lines if they do not __________________________ and are coplanar. Ø Skew lines-­‐ Two lines are skew lines if they do not intersect and are ________________ coplanar. Ø Parallel planes-­‐ Two ______________________ that do not intersect are parallel planes. Ø Transversal-­‐ A transversal is a line that intersects ____________________________ coplanar lines at different points. Example 1: Identify relationships in space Think of each segment in the figure as part of a line. Which line(s) or plane(s) in the figure appear to fit the description? a) Line(s) parallel to 𝐴𝐹 and containing point E. b) Line(s) skew to 𝐴𝐹 and containing point E. c) Line(s) perpendicular to 𝐴𝐹 and containing point E. d) Plane(s) parallel to plane FGH and containing point E. Geometry Chapter 3: Parallel and Perpendicular Lines Parallel and Perpendicular Lines: Two lines in the same plane are either parallel or intersect in a point. Through a point not on the line, there are infinitely many lines. Exactly one of these lines will be parallel to the given line, and exactly one of the lines will be perpendicular to the given line. Example 2: Identify Parallel and Perpendicular Lines Use the diagram at the right to answer each question. a) Name a pair of parallel line. b) Name a pair of perpendicular lines. c) Is 𝐴𝐵 ⊥ 𝐵𝐶? Explain. Geometry Chapter 3: Parallel and Perpendicular Lines v A transversal is a line that intersects two or more coplanar lines at different points. Angles Formed by Transversals Two angles are ___________________________ angles if they have corresponding positions. For example ∠2 𝑎𝑛𝑑 ∠6 are above the lines and to the right of the transversal t. Two angles are _____________________________________ angles if they lie between the two lines and on opposite sides of the transversal. Two angles are _____________________________________ angles if they lie outside the two lines and on opposite sides of the transversal. Two angles are _____________________________________ interior angles if they lie between the two lines and are on the same side of the transversal. Example 3: Identify Angle Relationships Identify all pairs of the following: a) Corresponding angles b) Alternate interior angles c) Alternate exterior angles d) Consecutive interior angles. Geometry Chapter 3: Parallel and Perpendicular Lines Practice: Think of each segment in the figure as part of a line. Which line(s) or plane(s) in the figure appear to fit the description? a) Line(s) parallel to 𝐶𝐷 and containing point A. b) Line(s) skew to 𝐶𝐷 and containing point A. c) Line(s) perpendicular to 𝐶𝐷 and containing point A. d) Plane(s) parallel to 𝐸𝐹𝐺 and containing point A. Identify all pairs of angles of the given type. a) Corresponding b) Alternate Interior c) Alternate Exterior d) Consecutive Interior Homework: 3.1 Practice B Skip #’s 29 & 30