By: Mitch Midea, Hannah Tulloch, Rosemary Zaleski

3-1   Parallel Lines- ═, are coplanar, never intersect   Perpendicular Lines- ┴, Intersect at 90 degree angles   Skew Lines- Not coplanar, not parallel, don’t intersect   Parallel Planes- Planes that don’t intersect

3-1 (cont.)   Transversal- ≠, a line that intersects 2 coplanar lines at 2 different points   Corresponding <s- lie on the same side of the transversal between lines   Alt. Int. <s- nonadjacent <s, lie on opposite sides of the transversal between lines   Alt. Ext. <s- Lie on opposite sides of the transversal, outside the lines   Same Side Int. <s- aka Consecutive int. <s, lie on the same side of the transversal between lines

3-1 Example Corresponding Angle Theorem

3-2   Corresponding <s Postulate- if 2 parallel lines are cut by a transversal, the corresponding <s are =   Alt. Int. < Thm.- if 2 parallel lines are cut by a transversal, the pairs of alt. int. <s are =   Alt. Ext. < Thm.- if 2 parallel lines are cut by a transversal, the 2 pairs of alt. ext. <s are =   Same Side Int. < Thm.- if 2 parallel lines are cut by a transversal, the 2 pairs of SSI <s are supp.

3-2 Examples Alternate Interior Angles Theorem Alternate Exterior Angles Theorem

3-3 Converses   Corresponding <s Thm.- if 2 coplanar lines are cut by a transversal so that a pair of corresponding <s are =, the 2 lines are parallel   Alt. Int. < Thm.- if 2 coplanar lines are cut by a transversal so that a pair of alt. int. <s are =, the lines are parallel   Alt. Ext. < Thm.- if 2 coplanar lines are cut by a transversal so that a pair of alt. ext. <s are =, the lines are parallel   SSI < Thm.- if 2 coplanar lines are cut by a transversal so that a pair of SSI < are =, the lines are parallel

3-3 Example ∠ JGH and ∠ KHG use the Same Side Interior Theorem

3-4 Perpendicular Lines   Perpendicular Bisector of a Segment- a line perpendicular to a segment at the segments midpoint   Use pictures from book to show how to construct a perpendicular bisector of a segment   The shortest segment from a point to a line is perpendicular to the line   This fact is used to define the distance from a point to a line as the length of the perpendicular segment from the point to the line

3-4 Example c d ab CD is a perpendicular bisector to AB, creating four congruent right angles

3-5 Slopes of Lines   Slope- a number that describes the steepness of a line in a coordinate plane; any two points on a line can be used to determine slope (the ratio of rise over run)   Rise- the difference in the Y- values of two points on a line   Run- the difference in the X- values of two points on a line

3-5 Example Slope is rise over run and expressed in equations as m

3-6 Lines in the Coordinate Plane   The equation of a line can be written in many different forms; point-slope and slope-intercept of a line are equivalent   The slope of a vertical line is undefined; the slope of a horizontal line is zero   Point-slope: y-y 1 = m(x-x 1 ) ; where m is the slope, and (x 1,y 1 ) is a given point on the line   Slope-intercept: y=mx+b : where m is the slope and b is the intercept   Lines that coincide are the same line, but the equations may be written differently

3-6 Example Slope-Intercept Form Point Slope Form