By: Mitch Midea, Hannah Tulloch, Rosemary Zaleski
3-13-1
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.)3-1 (cont.)Transversal- ≠, a line that intersects 2
coplanar lines at 2 different pointsCorresponding <s- lie on the same side of
the transversal between linesAlt. 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 Example3-1 Example
Corresponding Angle TheoremCorresponding Angle Theorem
3-23-2Corresponding <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 Examples3-2 Examples
Alternate Interior Angles Alternate Interior Angles TheoremTheorem
Alternate Exterior Angles Alternate Exterior Angles TheoremTheorem
3-33-3Converses
Corresponding <s Thm.- if 2 coplanar lines are cut by a transversal so that a pair of corresponding <s are =, the 2 lines are parallelAlt. Int. < Thm.- if 2 coplanar lines are cut by a transversal so that a pair of alt. int. <s are =, the lines are parallelAlt. Ext. < Thm.- if 2 coplanar lines are cut by a transversal so that a pair of alt. ext. <s are =, the lines are parallelSSI < Thm.- if 2 coplanar lines are cut by a transversal so that a pair of SSI < are =, the lines are parallel
3-3 Example3-3 Example
∠∠JGH and ∠KHG use the Same Side Interior JGH and ∠KHG use the Same Side Interior TheoremTheorem
3-43-4Perpendicular 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 Example3-4 Example
cc
dd
aa bb
CD is a perpendicular bisector to AB, CD is a perpendicular bisector to AB, creating four congruent right anglescreating four congruent right angles
3-53-5Slopes 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 lineRun- the difference in the X- values of two points on a line
3-5 Example3-5 Example
Slope is rise over run and expressed in equations Slope is rise over run and expressed in equations as as mm
3-63-6Lines 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 equivalentThe slope of a vertical line is undefined; the slope of a horizontal line is zeroPoint-slope: y-y1 = m(x-x1) ; where m is the slope, and (x1,y1) is a given point on the lineSlope-intercept: y=mx+b : where m is the slope and b is the interceptLines that coincide are the same line, but the equations may be written differently
3-6 Example3-6 Example
Slope-Intercept FormSlope-Intercept FormPoint Slope FormPoint Slope Form
