A. C. Given: D is the midpoint of BC of triangle ABC Prove: EF//BC E. 5. 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 3.Triangle ABC = triangle AEF 3.lf two angles of one triangle are equal respectively to two angles of another, then the triangle are similar. (a.a.) 4.AE + EB = AB & AF+FC = AC 4.Segment Addition Postulate %3D 5.Triangle BDE = triangle ADE & triangle CDF = triangle ADF 5.Definition of angle bisector %3D 6.Corresponding sides of similar triangles are proportional (C.S.S.T.P.) 6.AE/EB = AF/FC %3D 7.Angle ABD = angle AEF & angle BCA = 7.Corresponding Angles Postulate angle EFA %3D 8.DE bisects AB and DF bisects AC 8. proportionally 9. If a line divides two sides of a triangle proportionally, then it is parallel to the third side. (Theorem 54) 9.EF // BC ET !!

Question

Please help with the two-column proof

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

Image Transcription

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

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

Image Transcription

5. 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 3.Triangle ABC = triangle AEF 3.lf two angles of one triangle are equal respectively to two angles of another, then the triangle are similar. (a.a.) 4.AE + EB = AB & AF+FC = AC 4.Segment Addition Postulate %3D 5.Triangle BDE = triangle ADE & triangle CDF = triangle ADF 5.Definition of angle bisector %3D 6.Corresponding sides of similar triangles are proportional (C.S.S.T.P.) 6.AE/EB = AF/FC %3D 7.Angle ABD = angle AEF & angle BCA = 7.Corresponding Angles Postulate angle EFA %3D 8.DE bisects AB and DF bisects AC 8. proportionally 9. If a line divides two sides of a triangle proportionally, then it is parallel to the third side. (Theorem 54) 9.EF // BC ET !!

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