Geo, Chap 6 Practice Test, EV Ver 1
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1 Name: Class: _ Date: _ Geo, Chap 6 Practice Test, EV Ver 1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. (6-1) Which statement is true? a. All rectangles are squares. b. All parallelograms are quadrilaterals. c. All parallelograms are rectangles. d. All quadrilaterals are parallelograms. 2. (6-3) Which statement can you use to conclude that quadrilateral XYZW is a parallelogram? a. WN = NZ and YN = NX c. WZ XY and XW YZ b. WZ XY and XW WZ d. WZ ZY and XW YZ 3. (6-4) Which description does NOT guarantee that a quadrilateral is a parallelogram? a. a quadrilateral with consecutive angles supplementary b. quadrilateral with two opposite sides parallel c. a quadrilateral with the diagonals bisecting each other d. a quadrilateral with both pairs of opposite sides congruent 1
2 Name: 4. (6-6) Which diagram shows the most useful positioning of a square in the first quadrant of a coordinate plane? a. c. b. d. 5. (6-6) Which diagram shows the most useful positioning and accurate labeling of a rhombus in the coordinate plane? a. c. b. d. 2
3 Name: Short Answer 6. (6-1) Find the values of the variables and the lengths of the sides of this kite. 7. (6-1) What is the most precise name for quadrilateral ABCD with vertices A( 5, 2), B( 3, 6), C(4, 6), and D(2, 2)? 8. (6-2) LMNO is a parallelogram. If NM = x + 11 and OL = 3x + 7 find the value of x and then find NM and OL. 3
4 Name: 9. (6-2) For the parallelogram, if m 2 = 4x 28 and m 4 = 3x 9, find m 1. The diagram is not to scale. 10. (6-2) In parallelogram DEFG, DH = x + 4, HF = 4y, GH = 3x 1, and HE = 4y + 3. Find the values of x and y. The diagram is not to scale. 11. (6-3) Based on the information in the diagram, can you prove that the figure is a parallelogram? Explain. 4
5 Name: 12. (6-3) If ON = 5x 6, LM = 4x + 5, NM = x 9, and OL = 4y 8, find the values of x and y for which LMNO must be a parallelogram. The diagram is not to scale. 13. (6-4) In the rhombus, m 1 = 30x, m 2 = x + y, and m 3 = 3z. Find the value of each variable. The diagram is not to scale. 14. (6-4) DEFG is a rectangle. DF = 6x 2 and EG = x Find the value of x and the length of each diagonal. 15. (6-5) J and M are base angles of isosceles trapezoid JKLM. If m J = 16x + 7, and m M = 13x + 10, find m K. 5
6 Name: 16. (6-5) m R = 110 and m S = 90. Find m T. The diagram is not to scale. 17. (6-5) One side of a kite is 6 cm less than four times the length of another side. The perimeter of the kite is 70 cm. Find the lengths of the sides of the kite. 18. (6-6) In the coordinate plane, three vertices of rectangle HIJK are H(0, 0), I(0, d), and K(e, 0). What are the coordinates of point J? 19. (6-7) The vertices of the trapezoid are the origin along with A(4a, 4b), B(4c, 4b), and C(4d, 0). Find the midpoint of the midsegment of the trapezoid. 6
7 Geo, Chap 6 Practice Test, EV Ver 1 Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: L2 REF: 6-1 Classifying Quadrilaterals OBJ: Classifying Special Quadrilaterals STA: CA GEOM 12.0 KEY: reasoning kite parallelogram quadrilateral rectangle rhombus special quadrilaterals 2. ANS: C PTS: 1 DIF: L3 REF: 6-3 Proving That a Quadrilateral is a Parallelogram OBJ: Is the Quadrilateral a Parallelogram? STA: CA GEOM 7.0 CA GEOM 12.0 KEY: proof reasoning parallelogram 3. ANS: B PTS: 1 DIF: L3 REF: 6-4 Special Parallelograms OBJ: Is the Parallelogram a Rhombus or a Rectangle? STA: CA GEOM 7.0 CA GEOM 12.0 CA GEOM 13.0 KEY: square reasoning 4. ANS: D PTS: 1 DIF: L2 REF: 6-6 Placing Figures in the Coordinate Plane OBJ: Naming Coordinates KEY: algebra coordinate plane rectangle square 5. ANS: C PTS: 1 DIF: L3 REF: 6-6 Placing Figures in the Coordinate Plane OBJ: Naming Coordinates KEY: algebra coordinate plane isosceles trapezoid kite SHORT ANSWER 6. ANS: x = 8, y = 13; 11, 20 PTS: 1 DIF: L2 REF: 6-1 Classifying Quadrilaterals OBJ: Classifying Special Quadrilaterals STA: CA GEOM 12.0 TOP: 6-1 Example 3 KEY: algebra kite 7. ANS: parallelogram PTS: 1 DIF: L2 REF: 6-1 Classifying Quadrilaterals OBJ: Classifying Special Quadrilaterals STA: CA GEOM 12.0 TOP: 6-1 Example 2 KEY: kite parallelogram quadrilateral special quadrilaterals rectangle square trapezoid NOT: TC 07, Bimodal, Dynamic (pick up) 8. ANS: x = 2, NM = 13, OL = 13 PTS: 1 DIF: L2 REF: 6-2 Properties of Parallelograms OBJ: Properties: Sides and Angles STA: CA GEOM 7.0 CA GEOM 13.0 TOP: 6-2 Example 2 KEY: parallelogram algebra Theorem 6-1 1
8 9. ANS: 132 PTS: 1 DIF: L3 REF: 6-2 Properties of Parallelograms OBJ: Properties: Sides and Angles STA: CA GEOM 7.0 CA GEOM 13.0 TOP: 6-2 Example 2 KEY: algebra parallelogram opposite angles consectutive angles Theorem ANS: x = 4, y = 2 PTS: 1 DIF: L2 REF: 6-2 Properties of Parallelograms OBJ: Properties: Diagonals and Transversals STA: CA GEOM 7.0 CA GEOM 13.0 TOP: 6-2 Example 3 KEY: transversal diagonal parallelogram Theorem 6-3 algebra 11. ANS: Yes; the diagonals bisect each other. PTS: 1 DIF: L2 REF: 6-3 Proving That a Quadrilateral is a Parallelogram OBJ: Is the Quadrilateral a Parallelogram? STA: CA GEOM 7.0 CA GEOM 12.0 TOP: 6-3 Example 2 KEY: opposite angles parallelogram Theorem ANS: x = 11, y = 5 2 PTS: 1 DIF: L2 REF: 6-3 Proving That a Quadrilateral is a Parallelogram OBJ: Is the Quadrilateral a Parallelogram? STA: CA GEOM 7.0 CA GEOM 12.0 KEY: algebra parallelogram Theorem 6-7 opposite sides 13. ANS: x = 3, y = 87, z = 30 PTS: 1 DIF: L2 REF: 6-4 Special Parallelograms OBJ: Diagonals of Rhombuses and Rectangles STA: CA GEOM 7.0 CA GEOM 12.0 CA GEOM 13.0 TOP: 6-4 Example 1 KEY: algebra diagonal rhombus Theorem ANS: x = 10, DF = 58, EG = 58 PTS: 1 DIF: L2 REF: 6-4 Special Parallelograms OBJ: Diagonals of Rhombuses and Rectangles STA: CA GEOM 7.0 CA GEOM 12.0 CA GEOM 13.0 TOP: 6-4 Example 2 KEY: rectangle algebra Theorem 6-11 diagonal 15. ANS: 157 PTS: 1 DIF: L3 REF: 6-5 Trapezoids and Kites OBJ: Properties of Trapezoids and Kites STA: CA GEOM 7.0 CA GEOM 12.0 CA GEOM 13.0 KEY: algebra isosceles trapezoid base angles trapezoid Theorem
9 16. ANS: 70 PTS: 1 DIF: L2 REF: 6-5 Trapezoids and Kites OBJ: Properties of Trapezoids and Kites STA: CA GEOM 7.0 CA GEOM 12.0 CA GEOM 13.0 KEY: kite sum of interior angles 17. ANS: 8.2 cm and 26.8 cm PTS: 1 DIF: L2 REF: 6-5 Trapezoids and Kites OBJ: Properties of Trapezoids and Kites STA: CA GEOM 7.0 CA GEOM 12.0 CA GEOM 13.0 KEY: kite algebra word problem problem solving 18. ANS: (e, d) PTS: 1 DIF: L2 REF: 6-6 Placing Figures in the Coordinate Plane OBJ: Naming Coordinates TOP: 6-6 Example 2 KEY: coordinate plane algebra rectangle 19. ANS: (a + c + d, 2b) PTS: 1 DIF: L3 REF: 6-7 Proofs Using Coordinate Geometry OBJ: Building Proofs in the Coordinate Plane STA: CA GEOM 17.0 KEY: algebra coordinate plane isosceles trapezoid midsegment 3
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