8.6 Proportions and Similar Triangles

Triangle Proportionality Theorem

If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

If TU ll QS, then R

T

QS

U

US

RU

TQ

RT

>

>

Given AB ll ED, find EA

8

4

12

C

D

B

E

A

EA

12

4

8 8 EA = 4(12) 8 EA = 48 EA = 6

>

>

Converse of the Triangle Proportionality Theorem

Determining Parallels

Given the diagram, determine whether

MN || GH.

N HL

MG

1648

21

56

Proportionality Theorem If three parallel lines intersect two transversals,

then they divide the transversals proportionally.

UW = VX

WY XZ

U W Y

V XZ

7

Using Proportionality Theorems

Theorem 8.7 If a ray bisects an angle of a triangle, then it

divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.

If CD bisects <ACB,

Then AD = CA

DB CB

A

D

BC

9

Using Proportionality Theorems

Given CD=14, find DB.

C DB

915

A

DB

14

9

15

15 DB = 9(14)

15 DB = 126

DB = 8.4

Solve

20

108

f

Solve.

9 8

10

s

20

12

22

x

Find the value of JN.

L

N

J

M

K

16

3

18

Find the value of the variable.

33 q

11 9