6.6 Proportionality Theorems

HW pg. 400 #3­17 1

November 20, 2013

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Bellwork1. Verify that ABC~ DEF for the given information. ABC: AC=6, AB=9, BC=12; DEF: DF=2, DE=3, EF=4The ratios are = (3/1) so ABC~ DEF by SSS Sim Th.

2. Show that the triangles are similar and write a similarity statement.

6.6 Proportionality Theorems

HW pg. 400 #3­17 2

November 20, 2013

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6.6 Proportionality TheoremsTriangle Proportionality Theorem: If a line // to 1 side of a intersects the other 2 sides, then it divides the 2 sides proportionally.

Converse of TPT: If a line divides 2 sides of a proportionally, then it is // to the 3 sides.

Q

S

R

T

UIf TU // QS, then RT = RU TQ US

Q

S

R

T

U If RT = RU, then TU // QS TQ US

6.6 Proportionality Theorems

HW pg. 400 #3­17 3

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6.6 Proportionality Theorems

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Theorem 6.6: If 3 // lines intersect 2 transversals, then they divide the transversals proportionally.

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.

U

V X

WY

Z

l

m UW = VXWY XZ

C

A

D

B

AD = CADB CB

6.6 Proportionality Theorems

HW pg. 400 #3­17 5

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6.6 Proportionality Theorems

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HW pg. 400 #3‐17 all