obj. 36 similar triangle properties
DESCRIPTION
Use properties of similar triangles to find segment lengths. Apply proportionality and triangle angle bisector theorems.TRANSCRIPT
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=