## Theorem 6.6- If three parallel lines intersect two transversals, then they divide the transversals proportionally.

## Lines AB CD and EF are parallel. Lines GH and IJ are transversals

KL/PO = LM/ON

PROOF

Given: AB is parallel to CD, CD is parallel to EF

Auxiliary Line From Point K To Point N

Let Q be the intersection point of KN and LO

1. <NKM = <KNP 1. Alternate Interior Angles

<NKP = <KNM Thorem

2. Triangle KNM = Triangle NKP 2. AA similarity Postulate

3. ML/LK=NQ/QK and 3. Triangle Proportionality

NO/OP=NQ/QK Theorem

4. EC/CA=NO/OP 4. Transitive Property of

Congruence

PROOF

Given: AB is parallel to CD, CD is parallel to EF

Auxiliary Line From Point K To Point N

Let Q be the intersection point of KN and LO

1. <NKM = <KNP 1. Alternate Interior Angles

<NKP = <KNM Thorem

2. Triangle KNM = Triangle NKP 2. AA similarity Postulate

3. ML/LK=NQ/QK and 3. Triangle Proportionality

NO/OP=NQ/QK Theorem

4. EC/CA=NO/OP 4. Transitive Property of

Congruence

## Which statement is not true?

A. AB/BC=DE/EF

B. EF/DE=BC/AB

C. BC/CF=EF/CF

D. AB/AC=DE/CF

Answer: C

B. EF/DE=BC/AB

C. BC/CF=EF/CF

D. AB/AC=DE/CF

Answer: C