CK-12 Geometry - Second Edition

(Marvins-Underground-K-12) #1

7.5. Proportionality Relationships http://www.ck12.org


Theorem 7-8: If a ray bisects an angle of a triangle, then it divides the opposite side into segments that are
proportional to the lengths of the other two sides.


Example 6:Findx.


Solution: Because the ray is the angle bisector it splits the opposite side in the same ratio as the sides. So, the
proportion is:


9


x

=


21


14


21 x= 126
x= 6

Example 7:Algebra ConnectionDetermine the value ofxthat would make the proportion true.


Solution:You can set up this proportion just like the previous example.


5


3


=


4 x+ 1
15
75 = 3 ( 4 x+ 1 )
75 = 12 x+ 3
72 = 12 x
6 =x

Know What? RevisitedTo findxandy, you need to set up a proportion using parallel the parallel lines.


2640


x

=


1320


2380


=


1980


y

From this,x= 4760 f tandy= 3570 f t.

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