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Name _______________________________________ Date ___________________ Class __________________ Practice A Conditions for Parallelograms For each definition or theorem, tell what information you would need about the figure to conclude that the figure is a parallelogram. For some exercises, there is more than one correct answer, but give only one example per exercise. 1. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. _____________________________ 2. If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram. _____________________________ 3. If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram. ________________________________________________________________________________________ 4. If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram. ________________________________________________________________________________________ 5. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. (Hint: The diagonals of the figure are WY and XZ. ) ________________________________________________________________________________________ 6. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. _____________________________ A quadrilateral has vertices E(1, 1), F(4, 5), G(6, 6), H(3, 2). Complete Exercises 7–10 to tell whether EFGH is a parallelogram. 7. Plot the vertices and draw EFGH. 8. Use the Distance Formula: EF ________ HG ________ 9. Use the Slope Formula: slope of EF ________ slope of HG ________ 10. The answers to Exercises 8 and 9 prove that EFGH is a parallelogram. Which one of Exercises 1–6 states the theorem that you used? ________ This desk lamp has a circular base and a movable arm in the shape of a parallelogram. Use the figure to answer Exercises 11–13. 11. AD is vertical. Name another side of parallelogram ABCD that is also vertical. ________ 12. Because AD is attached to the base, AD stays vertical as the arm is moved. Tell what happens to BC as the arm is moved up or down. ________________________________________________________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry Name _______________________________________ Date ___________________ Class __________________ 2.Possible answer: Use the slope formula to find the slope of each side: slope of b b , slope of GH , slope EF ac ac b b of FG , slope of EH . ac ac Segments with equal slopes are parallel, so EF is parallel to GH and FG is parallel to EH. Therefore EFGH is a parallelogram. 3. 80 books 4. 92 books 5. 9 15 6. x 3x 7. 0 2x Reteach 1. 10 cm 3. 12 m 5. 62 7. 32 9. 36 11. 48 13. D(0, 3) Challenge 2. 70 4. 10 m 6. 18 m 8. 9 m 10. 36 12. 132 14. N(2, 4) 2. m7 3. 90° 4. m5 5. 180° 6. 180° 8. mDAB 10. supplementary 11. supplementary 12. Converse of the Same-Side Interior Angles 13. definition 14. Yes; explanations will vary. 15. No; the puck will have to land in the goal. 16. No; explanations will vary. Problem Solving 1. mC 135; mD 45 2. 15 in. 4. 65 6. H 3. 4.5 ft 5. B 7. D Reading Strategies 1. 100 mm 4. 42 5. 138 6. 12 in. 7. 18 in. 8. 12 in. 9. 24 in. 10. 36 in. CONDITIONS FOR PARALLELOGRAMS Practice A 1. W Y and X Z 2. WX ZY and WZ XY 3. Possible answer: W is supplementary to X and to Z. 4. Possible answer: WX ZY and 1. Triangle Sum 7. mCDA 9. 360° 3. 86 mm WX ZY 5. WY and XZ bisect each other. 6. WX ZY and WZ XY 7. 8. 5; 5 10. 4 9. 4 4 ; 3 3 11. BC 12. BC moves up or down but stays vertical. Practice B 1. ABCD is a parallelogram. mA mC 72 and mB mD 108 EFGH is not a parallelogram. HI 8.6 and FI 7.6. EG does not bisect HF . 3. No, the diagonals do not necessarily bisect each other. 4. Yes, the triangles with numbered angles are by AAS. By CPCTC, the parallel sides are congruent. 2. 138 Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry