Transcript Aim:

Aim: What are the Multiplication and Division postulates?
Do Now:
1
x4
5
2) What value of x makes the statement below true?
1) Solve for x:
x AB  CD
A
C
4 cm
B
24 cm
D
3) If M is the midpoint of AB, what value of x
makes the statement below true?
x AB  AM
A
M
Geometry Lesson:
Multiplication/Division Postulates
B
1
Multiplication If equal quantities are multiplied by equal
quantities, the products are equal.
Postulate:
If
a  b,
and c  d ,
then ac = bd
Given:
EG  RS
G is midpoint of EK
S is midpoint of RT
Prove: EK  RT
R
S
T
E
G
K
EG  RS
2 EG  2 RS
EK  2 EG
RT  2 RS
EK  RT
Given
Multiplication Postulate
Def. Midpoint
Def. Midpoint
Substitution Postulate
Geometry Lesson:
Multiplication/Division Postulates
2
Division If equal quantities are divided by equal
Postulate: quantities, the quotients are equal.
If a  b,
and c  d ,
Special Case: Halves of equal
quantities are equal.
a b
then =
c d
Given:
EK  RT
G is midpoint of EK
S is midpoint of RT
Prove: EG  RS
R
S
T
E
G
K
EK  RT Given
EK RT Division Postulate

2
2
EK Def. Midpoint
EG 
2
RT Def. Midpoint
RS 
2
Substitution Postulate
EG  RS
Geometry Lesson:
3
Multiplication/Division Postulates
Given:
Ex 1: AB  CD,
RS  2 AB, LM  2CD
Prove: RS  LM
R
S
A
B
L
M
C
D
Statements
Reasons
1)
AB  CD
1) Given
2)
RS  2 AB
2) Given
3)
LM  2CD
3) Given
4)
2 AB  2CD
5)
RS  LM
4) Multiplication Postulate
5) Substitution Postulate
Geometry Lesson:
Multiplication/Division Postulates
4
Given:
Ex 2: AB  DC
1
1
AF  AB, EC  DC
2
2
Prove: AF  EC
D
E
C
A
F
B
Statements
Reasons
AB  DC
1
1
AF  AB, EC  DC
2
2
1
1
AB  DC
2
2
1) Given
4)
AF  EC
4) Substitution Postulate
5)
AF  EC
5) Def. Congruent Segments
1)
2)
3)
2) Given
3) Division Postulate
Geometry Lesson:
Multiplication/Division Postulates
5
B
3)
ExGiven:
3, 4: BD  BE
BA  3BD, BC  3BE
D•
• E
Prove: BA  BC
A
C
4) Given: SRX  RSY ,
1
mSRY  mSRX
2
1
mRSX  mRSY
2
Prove: SRY  RSX
T
X
R
Geometry Lesson:
Multiplication/Division Postulates
Y
S
6
D
ExGiven:
5,6: DF  HB,
5)
DC  2 DF , AB  2 HB
Prove: DC  AB
F
E
A
G
H
1
1
BE  BD, AE  AC
2
2
Prove: BE  AE
B
C
D
6) Given: BD  AC
C
E
A
Geometry Lesson:
Multiplication/Division Postulates
B
7