Ch 5.3 Use Angle bisectors of triangles. In this section… We will use the properties of an angle bisector to solve for missing side lengths.

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Presentation transcript:

Ch 5.3 Use Angle bisectors of triangles

In this section… We will use the properties of an angle bisector to solve for missing side lengths.

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!

Angle Bisector?

Angle bisector? 5x x - 14

Angle bisector? 3x + 1 6x - 8

Page 313 #2 - 17

Point of Concurrency The 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 Incenter Problems 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!

Using the Incenter

Using the incenter

Page 314, #