Postulate 4

Angle Addition Postulate

For any angle PQR, if A is in the interior of PQR, thenmPQA + mAQR = mPQR.

2

1

A

R

P

Q m1 + m2 = mPQR.

There are two equations that can be derived using Postulate 4.

m1 = mPQR – m2

m2 = mPQR – m1

These equations are true no matter where A is locatedin the interior of PQR.

The Angle Addition PostulateThe Angle Addition Postulate

2x°

(5x – 6)°

B

DC

A

Find mABC and mCBD if mABD = 120.

mABC + mCBD = mABD Postulate 4

2x + (5x – 6) = 120 Substitution

7x – 6 = 120 Combine like terms

7x = 126

x = 18

Add 6 to both sides

Divide each side by 7

mABC = 2x

mABC = 2(18)

mABC = 36

mCBD = 5x – 6

mCBD = 5(18) – 6

mCBD = 90 – 6

mCBD = 84

36 + 84 = 120

The Angle Addition PostulateThe Angle Addition Postulate

PostulatesPostulates

Geometry is built on statements called _________.

Postulates are statements in geometry that are accepted to be true.

postulates

Postulate 5:A line contains at least 2 pointsA plane contains at least 3 points not all in one lineSpace contains at least 4 points not all in one line

Q

P

A

BC

PostulatesPostulates

Postulate 6: Two points determine a unique ___.

There is only one line that containsPoints P and Q

Q

P

Theorem 1-1: If two distinct lines intersect, then their intersection is a ____.

Lines l and m intersect at point T

Tl

m

Postulate 7: Three noncollinear points determine a unique _____.

There is only one plane that contains points A, B, and C.

A

BC

line

point

plane

PostulatesPostulates

A

BC

Points A, B, and C are noncollinear.

1) Name all of the different lines that can be drawn through these points.

AC�������������� �

CB�������������� �

BA�������������� �

2) Name the intersection of , and AC CB���������������������������������������� ���

Point C

PostulatesPostulates

1) Name all of the planes that are represented in the figure.

B

A

D

C

PostulatesPostulates

1) Name all of the planes that are represented in the figure.

There is only one plane that contains threenoncollinear points.

plane ABC (side)

B

A

D

C

plane ACD (side)

plane ABD (back side)

plane BCD (bottom)

PostulatesPostulates

Postulate 8: If two points are in a plane, then the lineThat contains the points is in that plane

The line that contains points A and B is in the plane shown.

A

B

M

PostulatesPostulates

N

D E

Postulate 9: If two distinct planes intersect, then their intersection is a ___.

Plane M and plane N intersect in line DE.

line

PostulatesPostulates

Name the intersection of plane CDG and plane BCD.

H

E F

G

CB

A D

PostulatesPostulates

Name the intersection of plane CDG and plane BCD.

DC�������������� �

H

E F

G

CB

A D

Name two planes that intersect in .DF�������������� �

planes ADF and CDF