SOL Practice Items 1. Let m represent: Angle A is obtuse. Let n represent: Angle B is obtuse. What is the symbolic representation of the following argument? Angle A is obtuse if and only if Angle B is obtuse. Angle A is obtuse or Angle B is obtuse. Therefore, Angle A is obtuse and Angle B is obtuse. 2. Lines a and b intersect lines c and d. Which statement could be used to prove a ∥ b and c ∥ d? A. ∠ 1 and ∠ 2 are supplementary and ∠ 5 ≅∠ 6. B. ∠ 1 ≅∠ 3 and ∠ 3 ≅∠ 5 C. ∠ 3 and ∠ 5 are supplementary, and ∠ 5 and ∠ 6 are supplementary D. ∠ 3 ≅∠ 4 and ∠ 2 ≅∠ 6 3. Line a passes through points with coordinates (-4,5) and (2,- 2). What is the slope of a line perpendicular to line a? Slope of perpendicular line =
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SOL Practice Items1. Let m represent:Angle A is obtuse. Let n represent:Angle B is obtuse.
What is the symbolic representation of the following argument?Angle A is obtuse if and only if Angle B is obtuse.Angle A is obtuse or Angle B is obtuse.Therefore, Angle A is obtuse and Angle B is obtuse.
2. Lines a and b intersect lines c and d.
Which statement could be used to prove a∥b and c ∥d?A. ∠1 and ∠2 are supplementary and ∠5≅∠6.B. ∠1≅∠3 and ∠3≅∠5C. ∠3 and ∠5 are supplementary, and ∠5 and ∠6 are supplementaryD. ∠3≅∠4 and ∠2≅∠63. Line a passes through points with coordinates (-4,5) and (2,-2).
What is the slope of a line perpendicular to line a?Slope of perpendicular line =
4. Which construction represents a correct first step in constructing a line segment perpendicular to JK through point P?5. Ben plans to bisect ∠ ABC to create the congruent angles ABD and CBD.Which angle is congruent to ∠ ABD and ∠CBD?
6. Given: Triangle ABC with vertices located atA(1,1), B(2,-3), C (-1, -4)Triangle ABC will be reflected over the line y = x. What will be the integral coordinates of point C’ after this transformation?
C’ ( , )
7. Given: Triangle ABC with AB = 42 and BC = 20Which of the following are possible lengths for AC?
12 20 22 32 42 50 62 708. Given: AB∥CD, AF ≅ FD
Prove: ∆ABF ≅ ∆DCFConstruct a proof. Statement Reason
9.Select the reasons for the last three statements of this proof.Given: ∠QSR≅∠TRS ; PR≅ PS
Prove ∆QSR ≅ ∆TRS
10. What value of x makes ∆STW ≅ ∆XYZ?
Directions: Draw a line from the selected reason to the correct box.
11. Given: AB∥CD
Prove: ∆ABF ∆DCFConstruct a proof.Statement Reason
12. For what value of x is ∆ABC ~ ∆DEF?
13. What is the total number of lines of symmetry for this figure?
14. A ladder leans against a wall. The bottom of the ladder is 10 feet from the base of the wall, and the top of the ladder makes an angle of 25° with the wall. Find the length, x, of the ladder.
15. Which of these regular polygons could tessellate a plane?Square Pentagon Octagon Hexagon Decagon
16. Quadrilateral QRST is to be reflected over the line y = -x
M
What are the coordinates of point T’ after this reflection?17. Given: Circle M with secants AB and AC
m∠A = 30°
If the length of arc BC is 3 cm, what is the circumference of the circle? 18. In circle O, m∠ SOT=68°
What is m∠ SRT?
19. In circle O, mFG=30° ,m BC=120°, and ∠J ≅∠K.
What is m EH?
20. Given: Three concentric circles with the center OKL≅ ln≅ NO Which is closest to the area? KP = 42 inches A. 231 sq. in.B. 308 sq. inC. 539 sq. in.D. 616 sq. in.
21. Bob divides his circular garden into 10 congruent sectors to plant different types of flowers. The circumference of Bob’s garden is 50.5 feet. What is the area of one sector of Bob’s garden?
22. Given: Circle T with WP = 36 centimeters.
Which best represents the area of the shaded sector? 23. The coordinate of the center of a circle are (-2,6). This circle has a diameter of 10 units. a. What is the equation of the circle?
b. Give the integral coordinates of two points that lie on the circle.
24. Given: Circle WW(-4,6)Radius = 10 units Which point lies on circle W?A. (0,4)B. (2,10)C. (4,0)D. (6,16)25. The equation of a circle is ( x−3 )2+( y+4 )2=16a. What are the coordinates of the center of the circle?
b. What is the radius of the circle?c. What is the diameter of the circle?d. Give the integral coordinates of two points that lie on the circle.
26. Circle O is defined by the equation x2+ ( y−2 )2=25. Plot the center if circle O and one point with integral coordinates that lies on circle O.
27.Two cylinders, a sphere, and a cone are shown. Select the two objects with the same volume.
Directions: Circle the two objects with the same volume.
28. A rectangular prism has a volume of 36 cm3a. If the height of the prism is tripled and the other dimensions do not change, what is the volume of the new rectangular prism?
b. If all dimensions of the original rectangular prism are tripled, what is the volume of the new rectangular prism?
29. A cylinder has a surface area of 96 square inches. If all dimensions of this cylinder are multiplied by to create a new cylinder, what will be ½the surface area of the new cylinder?
30. A company makes two similar cylindrical containers. The total surface area of the smaller container is 0.81 times that of the larger container. The height of the larger container is 60 centimeters. What is the height of the smaller container?
31.The ratio of the volume of two spheres is 8:27. What is the ratio of the lengths of the radii of these two spheres?
Directions: Write your number choices in boxes provided
32. A cylinder has a volume of 300π cubic centimeters and a base with a circumference of 10π centimeters. What is the height of the cylinder?
33. If the height of a rectangular prism is decreased by 13 , then which statement is true?A. The volume would decrease by 13B. The volume would decrease by 16C. The volume would decrease by 19D. The volume would decrease by 12734. The heights of two similar triangles are in ratio 2:5. If the area of the larger triangle is 400 square units, what is the area of the smaller triangle?
35. Line t contains the points (-4,7) and (5,-8).Plot a point other than point P with integral coordinates that lie on a line that is parallel to t and passes through point P.
Directions: Plot the point on the graph provided below.
36. Given: Quadrilateral ABCD.Which expression proves that ABCD is a rectangle?A. Then length of each diagonal is √r2+s2B. The common midpoint of the diagonals is ( r2 , s2 )C. The slope of AC is sr and the slope of BD is −srD. The length of both A B and CD is r and the length of both AD and BC is s.
37.The vertices of ∆ABC and the endpoints of DE have integral coordinates. Plot point F with integral coordinates so that ∆ABC ≅ ∆DEF.
Directions: Plot the point on the graph provided below.
38. Point A represents a vertex of an equilateral triangle inscribed in circle O.
Which other point is also a vertex of this equilateral triangle?
39. Directions: Shade the area indicated.
This Venn diagram represent the set of cell phones in a store. Let P represent the cell phones that take pictures. Let I represent the cell phones that connect to the Internet. Let G represent the cell phones that have games.Identify each region of the Venn diagram that represents the cell phones that only take pictures and have games.
40.This figure models a gate that has been constructed using two parallel vertical boards with a diagonal board connecting them. Identify all of the statements that must be true.
Directions: Circle all the statements that must be true.
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