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Name _______________________________________ Date ___________________ Class __________________ LESSON 6-3 Practice B Conditions for Parallelograms For Exercises 1 and 2, determine whether the figure is a parallelogram for the given values of the variables. Explain your answers. 1. 2. a 4.3 and b 13 ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ Determine whether each quadrilateral must be a parallelogram. Justify your answers. 3. 4. 5. ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ Use the given method to determine whether the quadrilateral with the given vertices is a parallelogram. 6. Find the slopes of all four sides: J(4, 1), K(7, 4), L(2, 10), M(5, 7) ________________________________________________________________________________________ ________________________________________________________________________________________ 7. Find the lengths of all four sides: P(2, 2), Q(1, 3), R(4, 2), S(3, 7) ________________________________________________________________________________________ 8. Find the slopes and lengths of one pair of opposite sides: J(2, 2), K(3, 3), L(1, 5), M(2, 0) ________________________________________________________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 6-20 Holt Geometry 7. PQ RS 26 ; QR PS 5 2 ; PQRS is a parallelogram. LESSON 6-3 Practice A 8. Possible answer: UV TW 2 5 ; slope of UV slope of TW 2; TUVW is a parallelogram. Practice C 1. W Y and X Z 2. WX ZY and WZ XY 3. Possible answer: W is supplementary to X and to Z. 1. A(4, 4), B(2, 5), C(2, 5), D(0, 26) 2. Possible answer: A C 4. Possible answer: WX ZY and WX ZY 3. AB || CD ; possible answer: because A B and C D and the sum of the interior angle measures of a quadrilateral is 360°, 2mA 2mD 360° or 2(mA mD) 360°. Therefore mA mD 180°. A and D are supplementary, so by the Converse of the Same-Side Interior Angles Theorem, AB || CD 5. WY and XZ bisect each other. 6. WX ZY and WZ XY 7. 8. 5; 5 10. 4 9. 4. All four sides are congruent, and the two pairs of opposite angles are congruent; possible answer: because the diagonals are perpendicular, all four angles created by the intersecting diagonals are right angles and therefore congruent. And because the diagonals bisect each other, all four of the right triangles are congruent by SAS. By CPCTC, all four of the parallelogram’s sides must be congruent. The two pairs of opposite angles are congruent as for any parallelogram. 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. 5. 4. Yes, the triangles with numbered angles are by AAS. By CPCTC, the parallel sides are congruent. 5. No, x x may not be 180. 6. slope of JK slope of LM 1; slope 2 of KL slope of JM 3 ; JKLM is a parallelogram. All four sides are congruent, and all four angles are congruent; possible answer: the sides are congruent for the same reasons given in Exercise 4. But because the diagonals are congruent and bisected, each right triangle.created by the diagonals is an isosceles right triangle. The acute angles of these triangles have measure 45°, so all the angles of the Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. A57 Holt Geometry Name _______________________________________ Date ___________________ Class __________________ parallelogram have measure 90°. 6. 90° Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 6-20 Holt Geometry