Pre-AP Geometry Worksheet Proving Parallelograms I. 1. Name___________________________ Write out what reason proves the following quadrilateral is a parallelogram. 2. 3. 20 100° 14 100° 14 20 II. For what value of x is the quadrilateral a parallelogram? 4. 5. 4x+2 x+7 2x+3 III. 7. 6. 6x 5x-6 Describe how to prove that ABCD is a parallelogram. 8. A D 9. A B D C IV. Which statement below is not necessarily true? 10. In quadrilateral WXYZ, WZ and XY are congruent and parallel. A) mY mW 180 B) X Z C) WX ZY A B D C D) WX 3x+2 ZY B C V. ERROR ANALYSIS 11. A student claims that because two pairs of sides are congruent, quadrilateral DEFG shown below is a parallelogram. Explain the error that the student is making. D 5 E 7 G 5 7 F VI. For what value of x is the quadrilateral a parallelogram? 12. 13. 14. 66° (x+10)° x° 66° (2x+20)° x° 3x° VII. Application 15. In the diagram, ABCD is a parallelogram, BF DE 12 , and CF 8 . Find AE . Explain your reasoning. A B F D E C VIII. A student claims incorrectly that the marked information below can be used to show that the figure is a parallelogram. Draw a quadrilateral with the marked properties that is clearly NOT a parallelogram. Explain your reasoning. 16. 17. 8 8 IX. Proofs 18. Given: A C , B D Prove: ABCD is a parallelogram. A B Hint: Let xo represent mA and mC . Let yo represent mB and mD . Write and simplify and equation and solve. D C 19. Given: Diagonals JL and KM bisect each other. Prove: JKLM is a parallelogram. K L P Statements Reasons J M

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