6. Which angles in the diagram are congruent to 1? Choose all that apply. 2. m YKZ
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1 PRYZ is a rhombus. If RK = 5, RY = 13 and m YRZ = 67, find each measure. Quadrilateral GHJK is a rectangle and m 1 = KY 6. Which angles in the diagram are congruent to 1? Choose all that apply. 2. m YKZ ALGEBRA Find the value of each variable in the given parallelogram. (2 points each) 7. Which angles in the diagram are congruent to 2? Choose all that apply Determine whether each quadrilateral is a parallelogram. Justify your answer. 4. MNPQ is a rhombus. If and AP = 3, find each measure. 5. CONSTRUCTION Mr. Rodriguez used the parallelogram at the right to design a herringbone pattern for a paving stone. He will use the paving stone for a sidewalk. If m 1 is 130, find m 2, m 3, and m m MNP 10. In rhombus XYZA, if 8, find. Powered by Cognero Page 1
2 11. In rhombus DEFG, if, find. 16. The diagonals of square ABCD intersect at E. If AE = 2x + 6 and BD = 6x 10, find AC. a. 11 b. 28 c. 56 d Find the values of x and y so that the quadrilateral is a parallelogram. Determine whether the quadrilateral is a parallelogram. Justify your answer. (2 points each) 12. a. x = 27, y = 90 b. x = 27, y = 40 c. x = 13, y = 90 d. x = 90, y = Find in parallelogram RSTW, if =2x-1 and m S=x+16 a. 17 b. 33 c. 55 d. 125 Indicate the answer choice that best completes the statement or answers the question. 13. The diagonals of square ABCD intersect at E. If AE = 3x 4 and BD = 10x 48, find AC. a. 90 b. 52 c. 26 d For parallelogram JKMH, find, and the value of x.,, 14. Find the value of x so that this quadrilateral is a parallelogram. 20. Determine whether this quadrilateral is a parallelogram. Justify your answer. a. 12 b. 24 c. 36 d Judith built a fence to surround her property. On a coordinate plane, the four corners of the fence are loc at ( 16, 1), ( 6, 5), (4, 1), and ( 6, 3). Which of the following most accurately describes the shape of Judi fence? a. square b. rectangle c. rhombus d. trapezo Powered by Cognero Page 2
3 21. If in rhombus ABCD, find the value of z. COORDINATE GEOMETRY Graph each quadrilateral with the given vertices. Determine whether the figure is a parallelogram. Justify your answer with the method indicated. 28. R( 2, 5), O(1, 3), M( 3, 4), Y( 6, 2); Distance and Slope Formulas 22. Given parallelogram ABCD with C(5, 4), find the coordinates of A if the diagonals and intersect at (2, 7). 23. The diagonals of square ABCD intersect at E. If AE = 2, find the perimeter of ABCD. Write true or false. 24. A parallelogram always has four right angles. 29. Determine whether the figure with the given vertices is a parallelogram. Use the method indicated. ; Slope Formula 30. PROOF Write a paragraph proof of the following. 25. Find x. 26. Determine whether ABCD is a parallelogram if AB = 6, BC = 12, CD = 6, and DA = 12. Justify your answer. 27. The slope of and is and the slope of Given: Prove: and 31. Write a two-column proof to show that opposite angles of a parallelogram are congruent: Given: GKLM is a parallelogram Prove: G L and K M and is. The best name for ABCD, using the given information, is a. Powered by Cognero Page 3
4 32. Write a two-column proof to show that consecutive angles of a parallelogram are supplementary: Given: GKLM is a parallelogram Prove: G & K are supplementary Refer to parallelogram ABCD to answer to following questions. 33. Do the diagonals bisect each other? Justify your answer and show all necessary work. Powered by Cognero Page 4
5 Answer Key x = 18, y = 9 4. x = 30, y = , 130, No; none of the tests for parallelograms are fulfilled Yes; A pair of opposite sides is both parallel and congruent. 13. b 14. c 15. c 16. c 17. a 28. Yes; see students work. 29. Yes 30. Proof: We are given and. Since opposite angles of a parallelogram are congruent, and. Since congruence of angles is transitive, the Transitive Property of Congruence GKLM is a parallelogram (given) 2. GK LM, GM KL (def of a parallelogram) 3. (consecutive interior angle theorem) 4. (Angles supplementary to the same angle are congruent) GKLM is a parallelogram (given) 2. (def of a parallelogram) 3. (consecutive interior angle theorem) 33. Yes; and 18. b 19. and. 20. No; none of the tests for s are fulfilled ( 1, 10) false Yes; opposite sides are congruent to each other. 27. Rectangle Powered by Cognero Page 5
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