Chapter 9 Summary

1
Chapter 9 Summary
November -December 2003
Geometry
Period 2
2
BY
Leonard
3
Notes for Viewing this Project

• I was unable to place the bar over the letters
  for a line segment. I hope you understand that
  where it is supposed to say segment AB, it just
  says AB.
• Next to each key term, I placed a P, T, or Q to
  show what topic it is from. P stands for
  Parallelism, T stands for Triangles, and Q stands
  for Quadrilaterals
• I had trouble picking what kind of background I
  would use for each slide, so I decided to make
  the background colorful and unique.

4
Key Terms
Skew lines 2 lines that are in different
planes and never intersect
P
Parallel when 2 lines are coplanar and
never intersect
P
Transversal a line that intersects 2 parallel
lines (T is the transversal in this
diagram)
P
Early Version of Exterior Angle Earl Warren
5
Key Terms Continued
Alternate interior angles nonadjacent angles on
the opposite sides of the transversal
that are in the interior of the lines
the trans- versal runs through
P
Corresponding angles angles on the same side of
the transversal, but one angle
is interior and the other is exterior.
P
Del Mars Diagonal 15th Street
6
More Key Terms
a
b
Quadrilateral the union of 4 segments
Q
c
d
Sides segments of a shape (for example, AD DC)
Q
Vertices where the segments meet each other (a,
b, c, d)
Q
Angles the combination of two segments (such as
)
ABC
Q
Convex when a line is able to connect any 2
points in a plane or figure with out going
out of the figure itself
Q
convex
Encinitas Median Moonlight Beach
7
Key terms continued
Opposite (in terms of quadrilaterals) the
description of sides that never intersect
or angles that do not have a common side
(such as AB CD and AD BC or ?A
? C and ? B ? D)
Q
Consecutive (in terms of quadrilaterals) the
description of sides that have a
common end point or angles that share
a common side (E.g. AB BC or ? D
? C)
Q
Diagonal (in terms of quadrilaterals) segments
joining 2 nonconsecutive vertices (AC
BD for example)
Q
Transversal Torrey Pines State Beach
8
Q
more key terms...
Parallelogram quadrilateral with both pairs of
opposites sides parallel
Trapezoid quadrilateral with one pair of
parallel sides
Bases (of a trapezoid) the parallel sides (AB
CD)
Median (of a trapezoid) segment joining
midpoints of nonparallel sides (the red
line)
Q
Rhombus a parallelogram with all sides
congruent
Rectangle a parallelogram with all angles right
angles
Square parallelogram with all congruent
sides and all right angles
Q
9
Key Terms...
Intercept the term used to describe when points
are on the transversal (Line A and B
intercept segment CD on the transversal)
P
Concurrent when lines contain a single point
which lies on all of them
T
Point of Concurrency the point which is
contained by all of the lines
T
10
Parallelism Proofs/Examples
11
PCA Corollary
PCA Corollary states that corresponding angles
created by 2 parallel lines cut by a
transversal are congruent
In other words if L1 and L2 are parallel,
then ? 3 and ? 4 are congruent
This is possible because of the PAI Theorem and
the Vertical Angle Theorem
12
Problem using the PCA Corollary
13
-ior
PAI
PAI Theorem
Parallelism
14
Example Using PAI Theorem
15
Quadrilateral Proofs/Examples
16
A Quadrilateral Theorem
In other words Because AC and BD bisect each
other,