Obj. 36 Similar Triangle Properties

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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=

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