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GeometryQ&A LibraryA. 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.Start your trial now! First week only $4.99!*arrow_forward*

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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.