http://www.ck12.org Chapter 7. Similarity
7.10 Proportions with Angle Bisectors
Here you’ll learn how to set up and solve proportions with angle bisectors.
What if you were told that a ray was an angle bisector of a triangle? How would you use this fact to find unknown
values regarding the triangle’s side lengths? After completing this Concept, you’ll be able to solve such problems.
Watch This
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Click image to the left for more content.CK-12 Foundation: Chapter7ProportionswithAngleBisectorsA
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Click image to the left for more content.James Sousa:Triangle Angle BisectorTheorem
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Click image to the left for more content.James Sousa:Using the Triangle Angle Bisector Theorem to Determine Unknown Values
Guidance
When an angle within a triangle is bisected, the bisector divides the triangle proportionally
By definition,
−→
ACdivides^6 BADequally, so^6 BAC∼=^6 CAD. The proportional relationship isCDBC=ADAB.Theorem: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.