in the figure 5.13 abcd is a parallelogram point e is on the ray ab such that be=ab then prove that line ed bisect seg bc at point f

Question

in the figure 5.13 abcd is a parallelogram point e is on the ray ab such that be=ab then prove that line ed bisect seg bc at point f

Answer 1

Statements                                     Reasons      

1. ABCD is a parallelogram            1. Given

2. AB ≅ CD                                      2. Opposite sides of a parallelogram are congruent.

3. AB = CD                                      3. If two segments are congruent, then they have equal measure.

4. BE = AB                                      4. Given

5. BE = CD                                      5. Transitive Property

6. BE ≅ CD                                      6. If two segments have equal measure, then they are congruent.

7. AB ll CD                                      7. Opposite sides of a parallelogram are parallel.

8. ∠AED ≅ ∠EDC                             8. Parallel lines form congruent alternate interior angles.

9. ∠DFC ≅ ∠BFE                              9. Vertical angles are congruent.

10. ΔBEF ≅ ΔCDF                           10. SAA

11. BF ≅ CF                                    11. CPCTC

12. F is the midpoint of BC           12. If a point divides a segment into two congruent parts, it is the midpoint                                                              of the segment.

13. ∴ ED bisects BC                       13. If a line passes through the midpoint of a segment, then it is a segment                                                              bisector.