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Lesson Notes 6.3 Proving that a Quadrilateral is a Parallelogram To prove a quadrilateral is a parallelogram, one of the following must be true: If this is true diagram algebra Theorem 6-5 Opposite sides are congruent WX ZY and XY WZ Then WXYZ is a parallelogram W Y and X Z Then WXYZ is a parallelogram XE EZ and WE EY Then WXYZ is a parallelogram Theorem 6-6 Opposite angles are congruent Theorem 6-7 Diagonals bisect each other Theorem 6-8 One pair of opposite sides is both congruent and parallel XW = YZ and XW || YZ Then WXYZ is a parallelogram OR XY = WZ and XY || WZ Then WXYZ is a parallelogram State whether the information given about quadrilateral SMTP is sufficient to prove that it is a parallelogram. 1. 2. 3. 4. 5. 6. Decide whether the quadrilateral is a parallelogram. Explain your answer. 13. 14. 15. 16. 17. 18. 19. 20. Algebra Find the values of x and y for which the figure must be a parallelogram. 7. 8. 9. Algebra Find the value of x. Then tell whether the figure must be a parallelogram. Explain your answer. 10. 11. 12.