1Geometry Lesson: Multiplication/Division Postulates

Aim:

Do Now:1) Solve for x:

2) What value of x makes the statement below true?

What are the Multiplication and Division postulates?

14

5x

A B

C D

4 cm

24 cmx AB CD

3) If M is the midpoint of AB, what value of x makes the statement below true?

A BM

x AB AM

2Geometry Lesson: Multiplication/Division Postulates

Multiplication Postulate:

If equal quantities are multiplied by equal quantities, the products are equal.

If ,

and ,

then =

a b

c d

ac bd

E KG

R TS

Given

2 2EG RSEG RS

Multiplication Postulate

2EK EG Def. Midpoint

Def. Midpoint2RT RSEK RT Substitution Postulate

G is midpoint of EKS is midpoint of RT

Given:

Prove: EK RT

EG RS

3Geometry Lesson: Multiplication/Division Postulates

Division Postulate:

If equal quantities are divided by equal quantities, the quotients are equal.

Given

Division Postulate

Def. Midpoint

Def. Midpoint

Substitution Postulate

EK RT

2

EKEG

2

RTRS

2 2

EK RT

EG RS

If ,

and ,

then =

a b

c d

a b

c d

Special Case: Halves of equal quantities are equal.

E KG

R TS

G is midpoint of EKS is midpoint of RT

Given:

Prove:

EK RT

EG RS

4Geometry Lesson: Multiplication/Division Postulates

Ex 1:

Statements Reasons

1) 1)

2) 2)

3) 3)

4) 4)

5) 5)

R

L M C

BAS

D

Given:

Prove:

,

2 , 2

AB CD

RS AB LM CD

RS LM

AB CD Given

2RS AB

2LM CDGiven

Given

2 2AB CD Multiplication Postulate

RS LM Substitution Postulate

5Geometry Lesson: Multiplication/Division Postulates

Ex 2:

Statements Reasons

1) 1)

2)2)

3) 3)

4) 4)

5) 5)

AB DC Given

ED

A F B

CGiven:

Prove:

AB DC1 1

, 2 2

AF AB EC DC

AF EC

1 1,

2 2AF AB EC DC Given

Division Postulate1 1

2 2AB DC

AF EC

Def. Congruent SegmentsAF EC

Substitution Postulate

6Geometry Lesson: Multiplication/Division Postulates

Ex 3, 4:• •

CA

B

D E

3) Given:

Prove:

3 , 3

BD BE

BA BD BC BE

BA BC

4) Given:

Prove: R S

YX

T,

1

21

2

SRX RSY

m SRY m SRX

m RSX m RSY

SRY RSX

7Geometry Lesson: Multiplication/Division Postulates

Ex 5,6:5) Given:

Prove:

CD

A BH

G

F

E,

2 , 2

DF HB

DC DF AB HB

DC AB

CD

A B

E6) Given:

Prove:

BD AC1 1

, 2 2

BE BD AE AC

BE AE