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

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