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October 19, 2015 3.1 Pairs of Lines and Angles Geometry 3.1 Pairs of Lines & Angles Essential Question What does it mean when two line are parallel, intersecting, coincident, or skew? October 19, 2015 3.1 Pairs of Lines and Angles Parallel Lines Coplanar lines that do not intersect. m || n m n Small arrows are used in a diagram to show lines are parallel. October 19, 2015 3.1 Pairs of Lines and Angles Skew Lines Lines that do not intersect and are not coplanar. s r October 19, 2015 3.1 Pairs of Lines and Angles Parallel Planes Planes that don’t intersect. October 19, 2015 3.1 Pairs of Lines and Angles Segments and Rays can be parallel. B Sketch the following examples. AB || CD D A C MN || OP M O N P October 19, 2015 3.1 Pairs of Lines and Angles Visualization B D AB and ED Parallel E A AB and EF Skew G AB and BD Perpendicular October 19, 2015 F Think of a rectangular box. 3.1 Pairs of Lines and Angles Example 1 Think of each segment in the figure are part of a line. Identify each pair of lines as parallel, skew E or perpendicular. F A Parallel B Perpendicular Perpendicular Skew October 19, 2015 G D C 3.1 Pairs of Lines and Angles L Your turn M Q P R N Name a ... Line parallel to Line perpendicular to Line skew to Plane parallel to plane RPL. Plane SNM October 19, 2015 S 3.1 Pairs of Lines and Angles Postulate 3.1 Parallel Postulate If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line. October 19, 2015 3.1 Pairs of Lines and Angles Postulate 3.2 Perpendicular Postulate If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line. October 19, 2015 3.1 Pairs of Lines and Angles Example 2 The given line markings show how the roads in a town are related to one another. Name a pair of parallel lines. 𝐷𝑀 𝑎𝑛𝑑 𝐹𝐸 Name a pair of perpendicular lines. 𝐷𝑀 𝑎𝑛𝑑 𝐵𝐹 Is No! October 19, 2015 3.1 Pairs of Lines and Angles Transversals A transversal is a line that intersects two or more coplanar lines at different points. t Transversal m n October 19, 2015 3.1 Pairs of Lines and Angles This is not a transversal. The lines intersect at only one point. October 19, 2015 3.1 Pairs of Lines and Angles Special Angle Pairs These are identified by their positions relative to one another. Learn to identify them and name them. These are listed on page 128 of the text. 1 2 4 3 5 6 8 7 October 19, 2015 3.1 Pairs of Lines and Angles Corresponding angles 1 & 5 2 & 6 1 2 4 3 3 & 7 4 & 8 5 6 8 7 October 19, 2015 3.1 Pairs of Lines and Angles Alternate Exterior Angles 1 & 7 2 & 8 1 2 4 3 5 6 8 7 October 19, 2015 3.1 Pairs of Lines and Angles Alternate Interior Angles 4 & 6 3 & 5 1 2 4 3 5 6 8 7 October 19, 2015 3.1 Pairs of Lines and Angles Same Side Interior Angles (Your book calls these Consecutive Interior Angles. We will use Same Side Interior.) 4 & 5 3 & 6 1 2 4 3 5 6 8 7 October 19, 2015 3.1 Pairs of Lines and Angles Abbreviations Corresponding Angles – Corr s Alternate Exterior Angles – Alt Ext s Alternate Interior Angles – Alt Int s Same Side Interior Angles – SS Int s October 19, 2015 3.1 Pairs of Lines and Angles Example 3 Identify the relationship. 4 and 10 Alt Ext s 5 and 8 SS Int s 8 and 6 Alt Int s 3 4 6 5 7 8 10 9 October 19, 2015 3.1 Pairs of Lines and Angles Your Turn Identify the relationship. 3 and 7 Corr s 9 and 5 Corr s 5 and 7 Alt Int s 3 4 6 5 7 8 10 9 October 19, 2015 3.1 Pairs of Lines and Angles Example 4 Identify all pairs of angles of the given type. Corresponding Alternate Interior Alternate Exterior Same Side Interior October 19, 2015 3.1 Pairs of Lines and Angles Example 4 Identify all pairs of angles of the given type. Corresponding 1 & 5, 2 & 6, 3 & 7, 4&8 Alternate Interior 2 & 7, 4 & 5 Alternate Exterior 1 & 8, 3 & 6 Same Side Interior 2 & 5, 4 & 7 October 19, 2015 3.1 Pairs of Lines and Angles If these lines are parallel, then why do they appear to intersect? Projective Geometry October 19, 2015 3.1 Pairs of Lines and Angles Assignment Pg. 129 #3 – 19 , 24 – 31 ALL October 19, 2015 3.1 Pairs of Lines and Angles