Chapter 5 Section 5.2

1. Chapter 5Section 5.2 Bisectors of Triangles

2. Theorem 5.5 Concurrency of the Perpendicular Bisectors of a triangle Theorem Theorem 5.5Concurrency of the Perpendicular Bisectors of a triangle The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle. The circumcenter is equidistant from the vertices of the triangle

3. Theorem 5.6 Concurrency of the Angle Bisectors of a triangle Theorem Theorem 5.6Concurrency of the Angle Bisectors of a triangle The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle. The incenter is equidistant from the sides of the triangle

4. A  B, BED  DFA, D is the circumcenter so it is equidistant from all the vertices of the triangle DA = 2 Since D is equidistant from A and B; AB = 4 A.A.S.

5. SVX  TVZ BisectsWZX Bisects WXZ WZX  WXZ V is the incenter so it is equidistant from all the sides of the triangle VS = 3 S.A.S. mVZX = 20

7. Sometimes Always Always Never

8. This distance can be found by using the Pythagorean Theorem Since the incenter is equidistant from each side of the triangle, this distance is the same 82 + x2 = 102 64 + x2 = 100 x2 = 36 x = 6 ID = 6

9. These two triangles are congruent by SAS DB = AD DB = 15