24. Select the correct proof from the options listed. Given: Quadrilateral DEFG with diagonals EG and DF; DF bisects EG at M; Z GEF = _ EGD Prove: DEFG is a parallelogram A Statements Reasons 1. Quadrilateral DEFG with diagonals 1. Given EG and DF; DF bisects EG at M. 2. EM = GM 2. Definition of a segment bisector 3. Z EMF = _ GMD 3. Vertical angles are congruent. 4. Z GEF = Z EGD 4. Given 5. A EMF = A GMD 5. Angle-Side-Angle 6. EF = DG 6. C.P.C.T.C 7. EF II DG 7. If two lines form congruent alternate interior angles with a transversal, then the lines are parallel. 8. DEFG is a parallelogram. 8. If one pair of sides of a quadrilateral are both parallel and congruent, then it is a parallelogram. B Statements Reasons 1. Quadrilateral DEFG with diagonals 1. Given EG and DF; DF bisects EG at M. 2. DM = FM 2. Definition of a diagonal of a parallelogram 3. Z EMF = Z GMD 3. Opposite angles are congruent. 4. Z GEF = Z EGD 4. Given 5. A EMF = A GMD 5. Angle-Angle-Angle 6. EF = DG 6. C.P.C.T.C 7. EF II DG 7. If two lines form congruent alternate exterior angles with a transversal, then the lines are parallel. 8. DEFG is a parallelogram. 8. If one pair of sides of a quadrilateral are both parallel and congruent, then it is a parallelogram.C. Statements Reasons 1. Quadrilateral DEFG with diagonals 1. Given EG and DF; DF bisects EG at M. 2. EM ~ GM 2. Definition of a bisector 3. Z EMF = / GMD 3. Opposite angles are congruent. 4. Z GEF = Z EGD 4. Given 5. A EMF - A GMD 5. Side-Side-Side 6. EF = DG 6. C.P.C.T.C 7. EF II DG 7. Parallel lines contain congruent angles. 8. DEFG is a parallelogram. 8. If one pair of sides of a quadrilateral are both parallel and congruent, then it is a parallelogram. D. Statements Reasons 1. Quadrilateral DEFG with diagonals 1. Given EG and DF; DF bisects EG at M. 2. EM = GM 2. Definition of a perpendicular bisector 3. Z EMF = Z GMD 3. Pairs of angles are congruent. 4. Z GEF = Z EGD 4. Given 5. A EMF = A GMD 5. Angle-Angle-Angle 6. EF = DG 6. Parallel lines of the parallelogram 7. EF II DG 7. If two lines form congruent alternate interior angles with a transversal, then the lines are parallel. 8. DEFG is a parallelogram. 8. Definition of a parallelogram E. None of the above