5.

B

E

p

A

F

C

Statements

Reasons

1.D is the midpoint of side BC of triangle

1.Given

ABC and the bisectors of angles ADB

and ADC meet AB and AC at E and F

respectively

3. Triangle ABC = triangle AEF

3.If two angles of one triangle are equal

respectively to two angles of another,

then the triangle are similar. (a.a.)

4.AE + EB = AB amp; AF+FC = AC

4.Segment Addition Postulate

5. Triangle BDE = triangle ADE amp; triangle

5. Definition of angle bisector

CDF = triangle ADF

6.AE/EB = AF/FC

6.Corresponding sides of similar

triangles are proportional (C.S.S.T.P.)

7.Angle ABD = angle AEF amp; angle BCA = |7.Corresponding Angles Postulate

angle EFA

8.DE bisects AB and DF bisects AC

8.

proportionally

9.EF // BC

9. If a line divides two sides of a triangle

proportionally, then it is parallel to the

third side. (Theorem 54)Math