Date: Sec 5-2 and 5-3 Concept: Bisector of a Triangle Objective: Given the properties of an angle bisector of a triangle, we will solve problems as measured by a s.g.

Circumcenter The point of concurrency of the perpendicular bisectors of a triangle Circumcenter

Thm 5.5 Concurrency of Perpendicular Bisector of a Triangle The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle PA=PB=PC

Example 1 Which point is the best spot for placing a sprinkler to water the plants located at x, y, and z? Look for the circumcenter

Example 1 - cont. Which point is the best spot for placing a sprinkler to water the plants located at x, y, and z? Point C If the sprinkler covers a circular region of 15 in, will the water reach all 3 plants? Yes, by thm 5.5, CZ=CY=CX and since CZ=10, the water would reach all the plants.

Incenter The point of concurrency of the angle bisectors of a triangle is called the incenter INCENTER

Thm 5.6: The point of concurrency of the angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle DO=DN=DP

Example: The anlge bis. Of  XYZ meet at pt P. (see diagram on board) 1. What segments are equal? TP=PU=PV 2. Find PT and PV. (use pyth. Thm.) PT=PV=5

Today’s Work