5

5.BEpAFCStatementsReasons1.D is the midpoint of side BC of triangle1.GivenABC and the bisectors of angles ADBand ADC meet AB and AC at E and Frespectively3. Triangle ABC = triangle AEF3.If two angles of one triangle are equalrespectively to two angles of another,then the triangle are similar. (a.a.)4.AE + EB = AB & AF+FC = AC4.Segment Addition Postulate5. Triangle BDE = triangle ADE & triangle5. Definition of angle bisectorCDF = triangle ADF6.AE/EB = AF/FC6.Corresponding sides of similartriangles are proportional (C.S.S.T.P.)7.Angle ABD = angle AEF & angle BCA = |7.Corresponding Angles Postulateangle EFA8.DE bisects AB and DF bisects AC8.proportionally9.EF // BC9. If a line divides two sides of a triangleproportionally, then it is parallel to thethird side. (Theorem 54)