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Geometry: Section 4.5
Name:
Objective: To define plane, coplanar, noncoplanar, transversal, alternate interior angles, alternate
exterior angles, corresponding angles and parallel lines.
Examples
plane Defn a surface such that if any two points \on the surface
are connected by a line, then all points of the line lie in the surface.
A plane has only two dimensions (no thickness) and is name by a Cursive
Upper Case letter or three noncollinear points in the plane.
It is drawn as a parallelogram.
Coplanar: Defn: points, lines, rays, etc. which lie entirely in the same
plane
Are two points always copalanar?
Are three points always coplanar?
Are four points always coplanar?
Are triangles always coplanar?
Noncoplanar: Defn: A line which intersects two coplanar lines in two
distinct points.
How many angles will a transversal always create with the two coplanar lines?
.
Interior Defn:: the region between the two coplanar lines which are cut by
a transversal..
Exterior Defn: the region not between the two coplanar lines which are cut by
a transversal
Alternate interior angles Defn: angles on opposite or slternate sides of
the transversal and inetween (in the interior) of the two lines.
Sometimes said to have a Z shape
Alternate exterior angles Defn: angles on opposite or slternate sides of
the transversal and not between (in the exterior) of the two
Corresponding angles: Def: Two angles in the same relative position
regarding the transversal and one of the two lines.
Sometimes called the F angles
Describe the numbered angles below.
\
C
1
D
2
A
B
A
C
D
F
D
3
4
A
B
5
B
E
C
Parallel lines: Defn: Two coplanar lines which do not intersect.
Segments, rays are parallel if they are parts of parallel lines or
if the lines containing them are parallel. We abbreviate parallel as
!##"
!##"
!##" !##"
!##" !##"
AB CD ! AB $ CD = " and AB and CD are coplanar.
Example
Skew lines: Defn: two lines which are
not coplanar
Example
Intersecting lines: Defn: two lines which have one pt in
common.
Example
Homework: 4.5 pg. 196-197 # 1-5
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