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