Secondary 2 Unit 7 Test Study Guide
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1 Class: Date: Secondary 2 Unit 7 Test Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which statement can you use to conclude that quadrilateral XYZW is a parallelogram? a. XY WZ and YZ XW c. XY YZ and YZ XW b. XY WZ and YZ ZW d. XN NY and ZN NW 2. Which description does NOT guarantee that a quadrilateral is a square? a. is both a rectangle and a rhombus b. has all right angles and has all sides congruent c. is a parallelogram with perpendicular diagonals d. has all sides congruent and all angles congruent 3. Which statement is true? a. All parallelograms are rectangles. b. All rectangles are parallelograms. c. All quadrilaterals are rectangles. d. All quadrilaterals are squares. 4. Which description does NOT guarantee that a quadrilateral is a kite? a. perpendicular diagonals, exactly one of which bisects the other b. perpendicular diagonals c. two distinct pairs of congruent adjacent sides d. one diagonal bisects opposite angles and the other diagonal does not 1
2 Short Answer 5. ABCD is a parallelogram. If m CDA = 69, then m DAB =?. The diagram is not to scale. 8. Find the values of a and b. The diagram is not to scale. 6. Find the measure of the numbered angles in the rhombus. The diagram is not to scale. 9. In parallelogram DEFG, DH = x + 1, HF = 4y, GH = 2x 5, and HE = 3y + 3. Find the values of x and y. The diagram is not to scale. 7. In rectangle PQRS, PR = 18x 29 and QS = x Find the value of x and the length of each diagonal. 10. LMNO is a parallelogram. If NM = x + 6 and OL = 2x + 4, find the value of x and then find NM and OL. 2
3 11. In quadrilateral ABCD, m ACD = 2x + 4 and m ACB = 5x 11. For what value of x is ABCD a rhombus? 13. If m B = m D = 44, find m C so that quadrilateral ABCD is a parallelogram. The diagram is not to scale. 12. Find the values of the variables and the lengths of the sides of this kite. 14. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale. 3
4 15. If ON = 5x 6, LM = 4x + 4, NM = x 5, and OL = 4y 3, find the values of x and y for which LMNO must be a parallelogram. The diagram is not to scale. 17. What is the most precise name for quadrilateral ABCD with vertices A( 3, 2), B( 1, 5), C(5, 5), and D(3, 2)? 16. Parallelogram ABCD has the angle measures shown. Can you conclude that it is a rhombus, a rectangle, or a square? Explain. 4
5 18. J and M are base angles of isosceles trapezoid JKLM. If m J = 15x + 3, and m M = 14x + 15, find m K. 20. For what values of x and y must this quadrilateral be a parallelogram? Find the lengths of the sides. The diagram is not to scale. 19. Find m 1 and m 3 in the kite. The diagram is not to scale. x = y = Side Lengths: 21. Give the name that best describes the parallelogram and find the measures of the numbered angles. The diagram is not to scale. 1 = 2 = 3 = 4 = 5
6 22. Judging by appearance, classify the figure in as many ways as possible using rectangle, square, quadrilateral, parallelogram, rhombus. 24. In quadrilateral ABCD, AE = x + 14 and BE = 3x 18. For what value of x is ABCD a rectangle? 23. Isosceles trapezoid ABCD has legs AB and CD, and base BC. If AB = 4y 5, BC = 4y 3, and CD = 5y 13, find the value of y. y = Long Answer 25. Write a paragraph proof to show that the base angles of an isosceles trapezoid are congruent. 6
7 26. Given: SV Ä TU and SVX UTX Prove: VUTS is a parallelogram 27. Is the quadrilateral a parallelogram? Explain. The diagram is not to scale. Answer (Circle One): Yes or No Explanation: 7
8 28. Explain how you can determine, without measuring any angles, whether a quadrilateral is a rectangle. 29. ABCD is a rhombus. Explain why ABC CDA. 30. Give a convincing argument that quadrilateral ABCD with A( 5, 4), B( 3, 2), C(5, 2), and D(3, 4) is a parallelogram. You can use the graph if neeeded to plot points and graph the shape. 8
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