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Use properties of similar triangles to find segment lengths. Apply proportionality and triangle angle bisector theorems.
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Obj. 36 Similar Triangle Properties
The student is able to (I can):
• Use properties of similar triangles to find segment lengths.
• Apply proportionality and triangle angle bisector theorems.
Triangle Proportionality Theorem
If a line parallel to a side of a triangle intersects the other two sides then it divides those sides proportionally.
S
P
A
C
E
>
>
PC SE�
AP AC
PS CE=
Note: This ratio is not the same as the ratio between the third sides!
≠AP PC
PS SE
Triangle Proportionality Theorem Converse
If a line divides two sides of a triangle proportionally, then it is parallel to the third side.
S
P
A
C
E
>
>
PC SE�
AP AC
PS CE=
Two Transversal Proportionality
If three or more parallel lines intersect two transversals, then they divide the transversals proportionally.
G
O
D
T
A
C>
>
>
CA DO
AT OG=
Examples Find PE
10x = (4)(14)
10x = 56
S
C
O
P
E
10101010 14141414
4444
10 14
4 x=
xxxx
28 3x 5 5.6
5 5= = =
>
>
Example Verify that
(15)(8) = (10)(12)?
120 = 120 � Therefore,
H
O
RSE
HE OS�
15
10
12 8
=15 10
?12 8
HE OS�
Example Solve for x.
6x = (10)(9)
6x = 90
x = 15
>
>
>
x
96
10
10 x
6 9=
