# A. C. Given: D is the midpoint of BC of triangle ABC Prove: EF//BC E. 6. Given: D is the midpoint of BC of triangle ABC Prove: EF//BC 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 2.Triangle ABC = triangle AEF 2.lf two angles of one triangle are equal respectively to two angles of another, then the triangle are similar. (a.a.) 3.AE + EB = AB & AF+FC = AC 3.Segment Addition Postulate 4.Triangle BDE = triangle ADE & triangle CDF = triangle ADF 4.Definition of angle bisector 5.AE/EB = AF/FC 5.Corresponding sides of similar triangles are proportional (C.S.S.T.P.) 6.Angle ABD = angle AEF & angle BCA = angle EFA 6.Corresponding Angles Postulate 7.DE bisects AB and DF bisects AC proportionally 8.EF II BC 8. If a line divides two sides of a triangle proportionally, then it is parallel to the third side. (Theorem 54) 7. 5.

Question

The proof is in the picture.

### Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Geometry

### Triangles

Transcribed Image Text

A. C. Given: D is the midpoint of BC of triangle ABC Prove: EF//BC E.

6. Given: D is the midpoint of BC of triangle ABC Prove: EF//BC 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 2.Triangle ABC = triangle AEF 2.lf two angles of one triangle are equal respectively to two angles of another, then the triangle are similar. (a.a.) 3.AE + EB = AB & AF+FC = AC 3.Segment Addition Postulate 4.Triangle BDE = triangle ADE & triangle CDF = triangle ADF 4.Definition of angle bisector 5.AE/EB = AF/FC 5.Corresponding sides of similar triangles are proportional (C.S.S.T.P.) 6.Angle ABD = angle AEF & angle BCA = angle EFA 6.Corresponding Angles Postulate 7.DE bisects AB and DF bisects AC proportionally 8.EF II BC 8. If a line divides two sides of a triangle proportionally, then it is parallel to the third side. (Theorem 54) 7. 5.