Geometry Chap 6 Practice Test Answers

Name: ______________________ Class: _________________ Date: _________ Geo, Chap 6 Practice Test 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 ____ 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. 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. 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. 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 + 48. 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. 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. Geo, Chap 6 Practice Test Answer Section MULTIPLE CHOICE 1. ANS: B KEY: reasoning | kite | parallelogram | quadrilateral | rectangle | rhombus | special quadrilaterals 2. ANS: C KEY: proof | reasoning | parallelogram 3. ANS: B KEY: square | reasoning 4. ANS: D KEY: algebra | coordinate plane | rectangle | square 5. ANS: C KEY: algebra | coordinate plane | isosceles trapezoid | kite SHORT ANSWER 6. ANS: x = 8, y = 13; 11, 20 KEY: algebra | kite 7. ANS: parallelogram KEY: kite | parallelogram | quadrilateral | special quadrilaterals | rectangle | square | trapezoid 8. ANS: x = 2, NM = 13, OL = 13 9. ANS: 132 KEY: parallelogram | algebra | Theorem 6-1 KEY: algebra | parallelogram | opposite angles | consectutive angles | Theorem 6-2 10. ANS: x = 4, y = 2 KEY: transversal | diagonal | parallelogram | Theorem 6-3 | algebra 11. ANS: Yes; the diagonals bisect each other. 12. ANS: x = 11, y = 5 2 13. ANS: x = 3, y = 87, z = 30 KEY: opposite angles | parallelogram | Theorem 6-8 KEY: algebra | parallelogram | Theorem 6-7 | opposite sides KEY: algebra | diagonal | rhombus | Theorem 6-13 14. ANS: x = 10, DF = 58, EG = 58 IF: 15. ANS: 157 16. ANS: 70 17. ANS: 8.2 cm and 26.8 cm 18. ANS: (e, d) 19. ANS: (a + c + d, 2b) KEY: rectangle | algebra | Theorem 6-11 | diagonal KEY: algebra | isosceles trapezoid | base angles | trapezoid | Theorem 6-15 KEY: kite | sum of interior angles KEY: kite | algebra | word problem | problem solving KEY: coordinate plane | algebra | rectangle KEY: algebra | coordinate plane | isosceles trapezoid | midsegment