CK-12 Geometry Concepts

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

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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.