7.10. Proportions with Angle Bisectors http://www.ck12.org
Example A
Findx.
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 B
Determine the value ofxthat would make the proportion true.
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
Example C
Find the missing variable:
Set up a proportion and solve like in the previous examples.
12
4
=
x
3
36 = 4 x
x= 9
Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.
CK-12 Foundation: Chapter7ProportionswithAngleBisectorsB
Vocabulary
Pairs of numbers areproportionalif they are in the same ratio. Anangle bisectoris a ray that divides an angle into
two congruent angles.