Name Class 6-2 Date Practice Form K Properties of Parallelograms Find the value of x in each parallelogram. 1. 129 x 51 To start, identify the relationship between the marked angles in the diagram. The marked angles are consecutive angles. By Theorem 6-4, the angles are supplementary. u 1 51 5 180 Then write an equation: x 2. 76 104 26 3. x 98 4. 154 x x 82 Algebra Find the values of the variables in $DEFG. D E 5. DG 5 2x 1 2, EF 5 3x 2 3, DE 5 3x 1 1, GF 5 2x 1 6 5 6. DG 5 4a, EF 5 5a 2 6, DE 5 3a 1 2, GF 5 2a 1 8 6 G F 7. DG 5 2r 1 3, EF 5 3r 2 3, DE 5 2r 1 6, GF 5 4r 2 6 6 8. DG 5 2t 2 10, EF 5 t 1 5, DE 5 t 1 15, GF 5 2t 15 Algebra Find the value of b in each parallelogram. Then find each side length or angle measure. 9. 6; 20.5; 11.7 10. b 14.5 15; 55; 125 (8s 5) 3b 6.3 (3s 10) 20.5 11. Developing Proof Complete this two-column proof. V U Given: ~QRST , ~TSVU S Prove: RQ > VU Reasons R T Q Statements 1) ~QRST , ~TSVU 1) 9 Given 2) RQ > ST , 9 ST O VU 2) Theorem 6-3 Opposite sides of ~ 3) RQ > VU 3) 9 Trans. Prop. of O Prentice Hall Foundations Geometry • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 15 Name Class Date Practice (continued) 6-2 Form K Properties of Parallelograms Algebra Find the value of each variable in each parallelogram. 12. 5 2h 2h 2 13. h5 14. 2d 1 11 2j 3 2 d3 3d 6 15. 5r 2j 3 4j 19 5r 2 4r 4 In the figure, GH 5 HI 5 IJ . Find each length. 16. EB 5 17. BD 10 18. AF 6.5 19. AK 19.5 20. CD 5 21. GJ 17.25 G E A B F 5.75 C 5 H I J D 6.5 K Find the value of a in each parallelogram. 22. 114 38 23. 11a 10 24. 15 (3a 5) 40 3a 110 25. The length of one side of a parallelogram is 3 more than twice the length of the adjacent side. The perimeter of the parallelogram is 30 cm. Find the lengths of the two adjacent sides of the parallelogram. 4 cm and 11 cm 26. Reasoning A classmate draws a parallelogram for which one side is twice as long as the other. If one side is 26 units, what are all the possible lengths of the perimeter? 78 units or 156 units Prentice Hall Foundations Geometry • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 16

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