5.2+Bisectors+of+a+Triangle

=Bisectors of a Triangle=

-pg. 272-278
In this lesson you will learn how certain segments and angles being bisected are parts of a triangle. You will use properties of a perpendicular bisector and angle bisector of a triangle.

__Vocabulary:__ __-concurrent lines-__ three or more lines that intersect at one point. __-point of concurrency-__ the point of intersection of concurrent lines. __-perpendicular bisector-__ a line, ray, or segment that is perpendicular to a side of the triangle at the midpoint of the side. __-circumcenter-__ the point of concurrency of the perpendicular bisectors of a triangle.

P is the circumcenter. For the acute triangle the circumcenter is inside the triangle, circumcenter for right is on the triangle, and the obtuse triangle circumcenter is outside the triangle.

__-angle bisector-__ a bisector of an angle of the triangle. point P is the incenter.



click here for extra help ↓ [] __[]

Examples:__ pg. 274 1. The angle bisectors of triangle MNP meet at point L. a. What segments are congruent? b. Find LQ and LR.

pg.275 2. The perpendicular bisectors of Δ//ABC// meet at point //G//. Find //GC//.

3. The angle bisectors of Δ//XYZ// meet at point //M//. Find //MK//.

__Answers:__ 1a. Theorem 5.6 says the three angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle. So,. 1b. Use the Pythagorean Theorem to find //LQ// in Δ//LQM//. So, //LQ// = 8 units. Because , //LR// = 8 units.

2. GC=7 3. MK=5

__Practice Problems__ @http://www.ccs.k12.in.us/chsteachers/WGerardot/Geometry/Chapter%205/Handouts/5.2%20HW.pdf @http://www.graves.k12.ky.us/schools/GCHS/tkluemper/5.2.pdf @http://www.docsroom.com/wp-content/uploads/2010/01/G51-53_YelloWS.pdf @http://www.wdeptford.k12.nj.us/High_School/kyeager/geometry%20docs/Chapter%2005/5.2%20practice_a.pdf