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## Geometry (all content)

### Unit 12: Lesson 4

Angle bisector theorem

# Using the angle bisector theorem

Sal uses the angle bisector theorem to solve for sides of a triangle. Created by Sal Khan.

## Want to join the conversation?

• why cant you just use the pythagorean theorem to find the side that x is on and then subtract the half that you know?
• The pythagorean theorem only works on right triangles, and none of these triangles are shown to have right angles, so you can't use the pythagorean theorem.
• At couldnt he also write 3/6 = 2/x or 6/3 = x/2? Thanks
• Yes, you could. switching the denominator and the numerator on both sides of an equation has no effect on the result. An example: If you have 3/6 = 3/6. Switch the denominator and numerator, and get 6/3 = 6/3. That is the same thing with x. 6/3 = x/2 can be 3/6 = 2/x. Now, when using the Angle Bisector theorem, you can also use what you just did. You will get the same result! Hope this answers your question.
• What's the purpose/definition or use of the Angle Bisector Theorem? Could someone please explain this concept to me?
• In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.
Consider a triangle ABC. Let the angle bisector of angle A intersect side BC at a point D. The angle bisector theorem states that the ratio of the length of the line segment BD to the length of segment DC is equal to the ratio of the length of side AB to the length of side AC:

http://en.wikipedia.org/wiki/Angle_bisector_theorem
• I'm still confused, why does this work?
• this may not be a mistake but when i did this in the questions it said i had got it wrong so clicked hints and it told me to do it differently to how Sal khan said to do it. is there a way of telling which one to use or have i missed something?
• That sort of thing has happened to me before. If you learn more than one correct way to solve a problem, you can decide which way you like best and stick with that one. I've learned math problems that required doing DOZENS of practice problems because I'd get all but the last one right over and over again. Study the hints or rewatch videos as needed. Keep trying and you'll eventually understand it. ;)
• I found the answer to these problems by using the inverse function like:
sin-1(3/4) = angleº
and got the correct answers but I know that these inverse functions only work for right triangles... can someone explain why this worked?
• The trig functions work for any angles. The right triangle is just a tool to teach how the values are calculated.
• not for this specifically but why don't the closed captions stay where you put them? They sometimes get in the way. The videos didn't used to do this.
• What is the angle bisector theorem?.
(1 vote)
• In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.