5.5 Properties of Parallelogram
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1 GEOMETRY Q2T6 5.5 Exam View WS Name: Class: Date: 5.5 Properties of Parallelogram True/False Indicate whether the statement is true or false. 1. In a parallelogram, the consecutive angles are congruent. Multiple Choice Identify the choice that best completes the statement or answers the question. Choose whether each statement is always true, sometimes true, or never true. 1. The consecutive angles of a parallelogram are supplementary. a. Always true b. Sometimes true c. Never true Completion Complete each statement. 1. The opposite angles of a parallelogram are. 2. The diagonals of a parallelogram each other. Name the most general polygon that fits each set of conditions. 3. A quadrilateral with opposite angles congruent: Mrs. Paunovska Page 1
2 GEOMETRY Q2T6 5.5 Exam View WS 4. x = y = a = b = 5. x = y = a = b = An Extra Credit Essay Question (*to be done on separate piece of paper) 1. Consider these points: A(1, 4), B(2, 12), C(9, 8). a. On a graph paper, graph the points. Add a fourth point D so that points A, B, C, and D are the vertices of a particular type of quadrilateral (can be a kite, trapezoid or parallelogram). Name the quadrilateral and use algebra to verify one of the properties of that type of quadrilateral. Show all your work. b. Find the coordinates of the point where the diagonals of quadrilateral ABCD intersect. Show all your work. For Every Quadrilateral you solve/ show you will get a 100 pts extra credit Mrs. Paunovska Page 2
3 5.5 Properties of Parallelogram Answer Section TRUE/FALSE 1. ANS: F PTS: 1 DIF: Easy REF: Lesson 5.5 TOP: Properties of Parallelograms KEY: parallelogram definition consecutive angles congruent MULTIPLE CHOICE 1. ANS: A PTS: 1 DIF: Easy REF: Lesson 5.5 TOP: Properties of Parallelograms KEY: parallelogram consecutive angles COMPLETION 1. ANS: congruent PTS: 1 DIF: Easy REF: Lesson 5.5 TOP: Properties of Parallelograms KEY: parallelogram opposite angles 2. ANS: bisect PTS: 1 DIF: Easy REF: Lesson 5.5 TOP: Properties of Parallelograms KEY: parallelogram diagonals 3. ANS: Parallelogram PTS: 1 DIF: Moderate REF: Lesson 5.5 TOP: Properties of Parallelograms KEY: parallelogram properties congruent opposite angles Mrs. Paunovska Page 1
4 4. ANS: 47, 133, 31, 38 PTS: 1 DIF: Moderate REF: Lesson 5.5 TOP: Properties of Parallelograms KEY: parallelograms 5. ANS: 49, 131, 30, 37 PTS: 1 DIF: Moderate REF: Lesson 5.5 TOP: Properties of Parallelograms KEY: parallelograms Mrs. Paunovska Page 2
5 ESSAY 1. ANS: 5 Points a. Point D, along with A, B, and C, forms a kite, trapezoid, or rhombus, and the quadrilateral is correctly identified. (Student may refer to the rhombus as a parallelogram.) To form a rhombus, point D must be (8, 0). For a kite, the point should satisfy y = 2x For a trapezoid, the point should satisfy either y = 4 7 x + 32 or y = 8x 64. Student correctly 7 verifies one of the following properties. For a kite, student verifies that the diagonals are perpendicular or (if he or she remembers the distance formula from algebra) that the quadrilateral has two distinct pairs of congruent consecutive sides. For a rhombus, student verifies one of the following properties: Both pairs of opposite sides are parallel, the diagonals are perpendicular, all four sides are congruent, or the diagonals bisect each other. (Verifying the last two properties requires using the distance formula.) For a trapezoid, student verifies that exactly one pair of opposite sides are parallel. b. Intersection point is correct. Work shows that student found equations for the two diagonals and then solved the system of equations. Here is the answer for the rhombus: Equation of diagonal AC: y = 0.5x Equation of diagonal BD: y = 2x + 16 To find x, set equations equal to each other: 2x + 16 = 0.5x = 2.5x x = 5 To find y, substitute 5 for x in one of the original equations: y = 2(5) + 16 y = 6 The diagonals intersect at point (5, 6). 3 Points Mrs. Paunovska Page 3
6 a. Point D, along with A, B, and C, forms a kite, trapezoid, or rhombus, and the quadrilateral is correctly identified. (Students may refer to the rhombus as a parallelogram.) Work shows that the method for verifying the chosen property is correct but includes algebraic errors. b. Work shows that student attempted to find the equations of the diagonals and solve the resulting system of equations, but answer is incorrect due to algebraic errors. 1 Point Answers are attempted but work includes significant errors. PTS: 5 DIF: Challenging REF: Lesson 5.3 Lesson 5.5 Lesson 5.6 OBJ: Discover properties of kites and trapezoids Discover properties of parallelograms Discover properties of rectangles, rhombuses, and squares TOP: Properties of Kites, Trapezoids, Parallelograms, and Special Parallelograms KEY: quadrilateral properties Mrs. Paunovska Page 4
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