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What is an angle bisector?An angle bisector is a line or ray
that divides an angle in half.
The distance from the angle bisector to each of the sides of the angle are congruent and perpendicular to the sides of the angles.
That can’t be the only thing we need to learn about angle bisectors!
Point of ConcurrencyThe angle bisectors will always
intersect at a point called the incenter.
If you draw perpendicular lines from that point to the sides of the triangle, then those segments are congruent.
Using the IncenterProblems that involve the incenter will
require you to at some point set some values equal to each other.
Because the incenter deals with perpendicular lines, that does open up the possibility of using the Pythagorean Theorem to solve for missing sides and then set values equal.
Perpendicular? Congruent? Sounds like some potential
Pythagorean Theorem stuff to me!