Transcript The Angle Addition Postulate For any angle PQR, if A is in the interior of PQR, then mPQA + mAQR = mPQR. P Postulate.

The Angle Addition Postulate
For any angle PQR, if A is in the interior of PQR, then
mPQA + mAQR = mPQR.
P
Postulate 4
Angle Addition
Postulate
1
Q
2
A
m1 + m2 = mPQR.
R
There are two equations that can be derived using Postulate 4.
m1 = mPQR – m2
m2 = mPQR – m1
These equations are true no matter where A is located
in the interior of PQR.
The Angle Addition Postulate
Find mABC and mCBD if mABD = 120.
mABC + mCBD = mABD
Postulate 4
2x + (5x – 6) = 120
Substitution
7x – 6 = 120
Combine like terms
7x = 126
Add 6 to both sides
x = 18
Divide each side by 7
36 + 84 = 120
C
mABC = 2x
mCBD = 5x – 6
mABC = 2(18)
mCBD = 5(18) – 6
mABC = 36
mCBD = 90 – 6
mCBD = 84
D
(5x – 6)°
2x°
A
B
Postulates
postulates
Geometry is built on statements called _________.
Postulates are statements in geometry that are accepted to be true.
Postulate 5:
A line contains at least 2 points
A plane contains at least 3 points not all in one line
Space contains at least 4 points not all in one line
P
Q
A
C
B
Postulates
Postulate 6:
line
Two points determine a unique ___.
P
Q
There is only one line that contains
Points P and Q
Theorem 1-1:
If two distinct lines intersect,
point
then their intersection is a ____.
l
T
m
Lines l and m intersect at point T
Postulate 7:
Three noncollinear points
plane
determine a unique _____.
There is only one plane that
contains points A, B, and C.
A
C
B
Postulates
Points A, B, and C are noncollinear.
A
1) Name all of the different lines that
can be drawn through these points.
AC
CB
BA
2) Name the intersection of AC , and CB
Point C
C
B
Postulates
1) Name all of the planes that are represented in the figure.
A
B
D
C
Postulates
1) Name all of the planes that are represented in the figure.
There is only one plane that contains three
noncollinear points.
plane ABC
(side)
plane ACD
(side)
plane ABD
(back side)
plane BCD
(bottom)
A
B
D
C
Postulates
Postulate 8:
If two points are in a plane, then the line
That contains the points is in that plane
The line that contains points A and B is in the
plane shown.
A
B
Postulates
Postulate 9:
line
If two distinct planes intersect, then their intersection is a ___.
Plane M and plane N intersect in line DE.
M
D
N
E
Postulates
Name the intersection of plane CDG and plane BCD.
F
E
A
H
B
D
G
C
Postulates
Name the intersection of plane CDG and plane BCD.
DC
Name two planes that intersect in DF.
planes ADF and CDF
F
E
A
H
B
D
G
C