Warm Up Week 7 Tell if the geometric figure can have a bisector. 1) angle 2) ray 3) line 4) segment 5) point

Geometry 5.2 Day 1 I will use properties of perpendicular bisectors of a triangle. A line ( or ray or segment ) that is perpendicular to a side of a triangle at the midpoint of that side. Perp Bisector of a Triangle Ex 1 Perp Bisector

Ex 2 Lines that intersect at the same point. Concurrent Lines Point of concurrency can be in, on, or outside the triangle. Rule 1

Concurrency of Perp Bisectors of a Triangle The perp bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle. Theorem 5.5 D E F G DE = DF = DG

Ex 3 DA = DB = DC A B C D

Ex 4 Three angle bisectors meet at point of concurrency. Angle Bisector of a Triangle The point of concurrency, and it always lies inside the triangle. Incenter

Concurrency of Angle Bisectors of a Triangle The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle. Theorem 5.6 PD = PE = PF P D E F

What is the length of LR? a 2 + b 2 = c 2 L Q S R M N P ( NQ ) 2 + ( LQ ) 2 = ( LN ) ( LQ ) 2 = ( LQ ) 2 = 289 ( LQ ) 2 = 64 LQ = 8 ≅≅ T5.6 LR = 8. ≅ so Ex 5

Do 1 : What is the distance from L to P? Handout - 5.2B Assignment L Q S R M N P 3 4