Name Class Date Practice 6-3 Form K Proving That a Quadrilateral Is a Parallelogram Algebra For what values of x and y must ABCD be a parallelogram? 1. 3x 5 A 7; 9 B 2y 6 y3 D C 2x 2 2x 4 2. A 3x 2 5 5 9 2x 1 2 A 3. 3; 6 B 11 To start, write an equation that relates the lengths of opposite sides that have algebraic expressions with the same variable. 2x 5 x9 y4 D 4. A 8x D C (y 87) 4y (7x 8) 12 2x 3 D 8; 29 B B 5. A D C 8y C 25; 10 10y B (4x 20) C Can you prove the quadrilateral is a parallelogram based on the given information? Explain. 6. 7. Yes; the diagonals bisect each other. 8. 9. 136 136 No; both sets of opposite angles need to be congruent. 44 Yes; an angle is supplementary to both of its consecutive angles. No; the same pair of sides needs to be both congruent and parallel. 10. Reasoning A classmate drew a quadrilateral with two diagonals. This divided the figure into four isosceles triangles. Is the quadrilateral a parallelogram? Use a drawing to justify your answer. Yes; since all the sections of the diagonals are congruent, the diagonals bisect each other and the figure is a parallelogram. Prentice Hall Foundations Geometry • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 25 Name Class Date Practice (continued) 6-3 Form K Proving That a Quadrilateral Is a Parallelogram 11. Developing Proof Complete this two-column proof of Theorem 6-8. A Given: AB > CD and BC > DA B Prove: ABCD is a parallelogram. C D Statements 1) Draw diagonal AC. Reasons 1) Definition of a diagonal 2) AB > CD and BC > DA 2) 9 Given 3) AC > AC 3) 9 Reflexive Prop. of O 4) nABC > 9 kCDA 4) 9 SSS 5) /B > 9 lD 5) 9 CPCTC 6) Draw diagonal BD. 6) Definition of a diagonal 7) BD > BD 7) 9 Reflexive Prop. of O 8) nBCD > 9 kDAB 8) 9 SSS 9) /A > 9 lC 9) 9 CPCTC 10) ABCD is a parallelogram. 10) 9 Theorem 6-10 12. Error Analysis A classmate said that a quadrilateral is a parallelogram only if one angle is supplementary to all the others. What is your classmate’s error? Explain. One l must be suppl. to both of its consecutive '. The classmate is describing a rectangle, which is one type of parallelogram. For what values of the variables must ABCD be a parallelogram? 13. 4x 9 A 2y 3 D 15. 12; 14 B 14. y 14 2x 1 A B (4x 8) D 2y 3x 3 (7y 3) D C C 4x 2 16. A 21.5; 39 (3y 15) B (2x 4) 6x 18 Prentice Hall Foundations Geometry • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 26 B 9; 18 3y 22 D C 3x 3 2y 2 A 7; 3 C

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