Transcript 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
b
a
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