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.