Transcript Document 7188008

BY
Leonard
•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.
Key Terms
Skew lines: 2 lines that are in different
planes and never intersect
Parallel: when 2 lines are coplanar and
never intersect
Transversal: a line that intersects 2 parallel lines
(T is the transversal in this diagram)
Early Version of Exterior Angle Earl Warren
Key Terms Continued
Alternate interior angles: nonadjacent angles on the opposite
sides of the transversal that are in
the interior of the lines the transversal runs through
Corresponding angles: angles on the same side of
the transversal, but one
angle is interior and the
other is exterior.
Del Mar’s Diagonal 15th Street
More Key Terms
a
Quadrilateral: the union of 4 segments
d
b
c
Sides: segments of a shape (for example, AD & DC)
Vertices: where the segments meet each other (a, b, c, d)
Angles: the combination of two segments (such as ABC )
Convex: when a line is able to connect any 2 points in a plane or
figure with out going out of the figure itself
convex
Encinitas Median Moonlight Beach
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)
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)
Diagonal (in terms of quadrilaterals): segments joining 2
nonconsecutive vertices (AC &
BD for example)
Transversal Torrey Pines State Beach
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)
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
Intercept: the term used to describe when points are on the transversal
(Line A and B intercept segment CD on the transversal)
Concurrent: when lines contain a single point which
lies on all of them
Point of Concurrency: the point which is contained by all of the lines
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
-ior
In other
words:
Because
AC and
BD
bisect
each
other, •
A
BCD is
a
parallelogram
Theorem: If there is one right angle in a parallelogram,
then it has 4 right angles, which means that parallelogram is a
rectangle.
In other words: If <D
is a right angle
and •
ABCD is a
parallelogram, then
<A, <B, and <C are
right angles, which
means that •
ABCD
is a rectangle.
This is because of the theorem that states
interior angles on the same side of the
transversal are supplementary and the theorem
that states supplementary congruent angles are
right angles.
180° Triangle Theorem: The sum of a triangle’s angles is 180.
a
c
b
80 °
60 °
150 °
50°
50 °
90 °
30 °
15 °
All of these triangles’ angles’ sum of measures is 180.
15 °
If a segment is between the midpoints on both
sides of a triangle, then that segment is 1) parallel
to the base and 2) half as long as the base.
a
x
c
In other words: If AX=XE and AY=YB,
then XY is parallel to CB
and XY=CB.
y
b
This can be proved by
using SAS, AIP,
Definition of a
Parallelogram, and a
couple parallelogram
theories.