This document discusses proportionality theorems in geometry. It introduces the Triangle Proportionality Theorem, which states that if a line is parallel to one side of a triangle, it divides the other two sides proportionally. It also discusses the converse of this theorem. Additionally, it presents Theorem 6.6, which says that if three parallel lines intersect two transversals, they divide the transversals proportionally. Finally, it introduces Theorem 6.7, which states that if a ray bisects an angle of a triangle, it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.
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1. 6.6 Proportionality Theorems November 21, 2011
Bellwork
1. Verify that ABC~ DEF for the given information.
ABC: AC=6, AB=9, BC=12; DEF: DF=2, DE=3, EF=4
The ratios are = (3/1) so ABC~ DEF by SSS Sim Th.
2. Show that the triangles are similar and write a similarity statement.
HW pg. 400 #317 all 1
2. 6.6 Proportionality Theorems November 21, 2011
6.6 Proportionality Theorems
Triangle Proportionality Theorem: If a line // to 1 side of a
intersects the other 2 sides, then it divides the 2 sides proportionally.
Q
T
R
If TU // QS, then RT = RU
U TQ US
S
Converse of TPT: If a line divides 2 sides of a proportionally, then it
is // to the 3 sides.
Q
T
R
If RT = RU, then TU // QS
U
S
TQ US
HW pg. 400 #317 all 2
4. 6.6 Proportionality Theorems November 21, 2011
Theorem 6.6: If 3 // lines intersect 2 transversals, then
they divide the transversals proportionally.
Y l
W
U
UW = VX
m WY XZ
V X Z
Theorem 6.7: If a ray bisects an < of a , then it divides
the opposite side into segments whose lengths are
proportional to the lengths of the other 2 sides.
A
D AD = CA
DB CB
B
C
HW pg. 400 #317 all 4
