Transcript THEOREMS & POSTULATES

SOME THEOREMS AND POSTULATES
Fernando Rodriguez
Buena Park HS
[email protected]
Presented at CMC South
Palm Springs, CA
Nov. 4, 2005
Postulate 2
Segment Addition Postulate
If B is between A and C, then AB + BC = AC.
If AB + BC = AC, then B is between A and C.
|
A
|
|
AC
B
AB
|
C
BC
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A segment bisector is a segment, ray, line, or
plane that intersects a segment at its midpoint.
A
M
B
M is the midpoint of AB if M is on AB and AM = MB.
C
M
A
B
D
CD is a bisector of AB.
Bisecting An Angle
An angle bisector is a
ray that divides an
angle into two
adjacent angles that
are congruent. In the
diagram ray CD
bisects ABC
because it divides the
angle into two
congruent angles,
_____ and _____.
A
D
C
B
mACD  mBCD
To write “ AB is Parallel to CD “
A
C
you write AB || CD
B
D
Parallel and Perpendicular Postulates
POSTULATE 13
Parallel Postulate
If there is a line and a point not on the line, then there is
exactly one line through the point parallel to the given
line.
P

There is exactly one line
through P parallel to  .
Parallel and Perpendicular Postulates
POSTULATE 14
Perpendicular Postulate
If there is a line and a point not on the line, then there is
exactly one line through the point perpendicular to the
given line.
P

There is exactly one line
through P perpendicular to
.
Given that m1  32, find each measure. Tell which postulate
or theorem you use.
a. m2
b. m3
c. m4
d. m5
m2  32 Corresponding Angle Postulate
m3  32 Alternate Exterior Angle Postulate
m4  1803  148 Linear Pair Postulate
m5  32 Vertical Angle Theorem
1
5
4
3
2
Theorem 5.9 Midsegment theorem
The segment connecting the midpoints of two sides of a
triangle is parallel to the third side and half as long
C
H
I
B
A
HI AB
1
HI    AB
 2