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CHAPTER 3 By: Team 2 Mr. Larose Block 1 3-1 Lines & Angles • Lines: – Parallel lines- coplanar lines that don’t intersect. – Skew lines- non-coplanar lines that are not parallel and do not intersect. – Parallel Planes- are planes that do not intersect. – Transversal- a line that intersects two or more coplanar lines. 3-1 Lines & angles. • Angles – Alternate interior angles- are nonadjacent interior angles that lie on opposite sides of the transversal. – Same-side interior angles- interior angles that lie on the same side of the transversal. – Corresponding- are on the same side of the transversal and are in corresponding positions. – Alternate exterior angles- nonadjacent exterior angles that are on opposite side of the transversal • Blue- Parallel lines • Red- Transversal • -Alternate interior angles • -Same-side interior angles • -Corresponding angles • -Alternate exterior angles 3-2 Properties of parallel lines • If two parallel lines are cut by a transversal, then – Corresponding angles, alternate interior angles, and alternate exterior angles are congruent – Same-side interior angles are supplementary Which angles are congruent to • • • -(Corresponding) -(Alternate Interior) -(Vertical) 3-3 Proving lines parallel • If two lines and a transversal form – Congruent corresponding angles – Congruent alternate interior angles – Congruent alternate exterior angles or – Supplementary same-side interior angles Then the two lines ARE PARALLEL. 3-4 Parallel & Perpendicular lines – Two lines parallel to the same line are parallel to each other. – In a plane, two lines perpendicular to the same line are parallel. – In a plane, if one line is perpendicular to one of two lines parallel lines then it is perpendicular to both parallel lines. 3-5 Parallel lines & Triangles - The sum of the measures of the angles of a triangle is 180. - The measure of the each exterior angle of a triangle equals the sum of the measures of its two remote interior angles. 3-6 Constructing parallel & Perpendicular lines • You can use a compass and a straightedge to construct – A line parallel to a given line through a point not on the line – A line perpendicular to a given line through a point on the line, or through a point not on the line 3-7 Equations of lines in the Coordinate plane • Slope-Intercept form is y =mx + b where m is the slope and b is the Y-intercept. • Point-slope form is y- y1=m(x-x1) where m is the slope and (x1,y1) is a point on the line. 3-8 Slopes of parallel and Perpendicular lines • Parallel lines have the same slope • The product of the slopes of two perpendicular lines is -1.