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# Angle Bisectors - Concept

###### Brian McCall

###### Brian McCall

**Univ. of Wisconsin**

J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

An angle is formed by two rays with a common endpoint. The **angle bisector** is a ray or line segment that bisects the angle, creating two congruent angles. To construct an angle bisector you need a compass and straightedge. Bisectors are very important in identifying corresponding parts of similar triangles and in solving proofs.

In a triangle if you draw in one of your angle bisectors, remember there's three, one for each vertex, you're going to divide the opposite side proportionally. Well, we could write two different ratios here and I'm going to explain what I mean by opposite side. If I look at this as my vertex and I'm bisecting it the side that's opposite to it, is going to be that opposite side the one that contains x and y here.

So I can say that the ratio of a:x so I'm going to write the ratio of a:x has to be equal to the ratio of b:y. Another way of looking at it is what's the relationship between a and b. I can say that a goes to b the way x goes to y.

So when you homework around a test you're going to see a problem where you have a triangle with an angle bisector and you're going to be trying to find some of these missing lengths. Remember that it will divide this opposite side proportionally.

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###### Brian McCall

B.S. in Chemical Engineering, University of Wisconsin

J.D. University of Wisconsin Law School (magna cum laude)

He doesn't beat around the bush. His straightforward teaching style is effective and his subtle midwestern accent is engaging. There's never a dull moment with him.

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## Comments (1)

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## Christy Chester · 10 months, 4 weeks ago

I appreciate the clear and simple way this material is presented. Thanks! :)