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Chapter 3 Geometry Powerpoint. 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
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Chapter 3 Geometry Powerpoint 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 a b d 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-y1 = m(x-x1) ; where m is the slope, and (x1,y1) 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 Point Slope Form Slope-Intercept Form
