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Praxis Mathematics: Geometry

Figures, measurement, coordinates, and right-triangle trigonometry for secondary mathematics, including decisions about student work.

Teacher certification exams are administered by testing organizations. FreeExam is not affiliated with those organizations, and these questions are original practice, not an official test.

Praxis is a trademark of Educational Testing Service. FreeExam is not affiliated with Educational Testing Service, and these questions are original practice, not an official test.

  1. 1.A right triangle has legs 6 and 8. What is the hypotenuse?

  2. 2.A triangle has base 10 and height 4. What is its area?

  3. 3.A circle has radius 5. Which expression is its circumference?

  4. 4.A student uses the diameter, 10, as the radius when finding the area of a circle and gets 100π. What is the area?

  5. 5.Two similar triangles have a scale factor of 3. A side of the smaller triangle is 4. What is the corresponding side of the larger?

  6. 6.A rectangular prism is 2 by 3 by 4. What is its volume?

  7. 7.Two angles of a triangle measure 40° and 70°. What is the third angle?

  8. 8.An exterior angle of a triangle is adjacent to a 50° interior angle. The other two interior angles are 60° and 70°. What is that exterior angle?

  9. 9.Two parallel lines are cut by a transversal. One corresponding angle is 35°. What is the other corresponding angle in that pair?

  10. 10.What is the distance between (0, 0) and (3, 4)?

  11. 11.What is the midpoint of (2, 6) and (8, 10)?

  12. 12.A student finds the slope between (1, 2) and (4, 8) as (1 − 4)/(2 − 8). What is the slope, and what was swapped?

  13. 13.Which equation is a circle of radius 4 centered at the origin?

  14. 14.A cylinder has radius 3 and height 5. Which expression is its volume?

  15. 15.In a 30-60-90 triangle, the side opposite 30° is 5. What is the hypotenuse?

  16. 16.A right triangle has an acute angle of 40° and hypotenuse 10. Which ratio equals the side opposite the 40° angle, divided by 10?

  17. 17.A square has side 7. What is its area?

  18. 18.A rectangle is 5 by 12. What is the length of a diagonal?

  19. 19.An isosceles right triangle has a leg of 6. What is the hypotenuse?

  20. 20.A student says all rectangles are squares. Which counterexample should the teacher draw?

  21. 21.What is the area of a circle with radius 6?

  22. 22.A central angle is 90° in a circle of radius 8. What fraction of the circle's area is the sector?

  23. 23.An inscribed angle intercepts an arc of 80°. What is the inscribed angle?

  24. 24.A translation moves every point 3 units right and 1 unit down. Where does (2, 5) go?

  25. 25.A reflection across the x-axis sends (3, −2) to which point?

  26. 26.A rotation of 90° counterclockwise about the origin sends (1, 0) to which point?

  27. 27.The base angles of an isosceles triangle are 55° each. What is the vertex angle?

  28. 28.A student claims two triangles are congruent because they have the same three angles. What is missing?

  29. 29.What is the surface area of a cube with edge 3?

  30. 30.A cone and a cylinder have the same radius and the same height. How do their volumes compare?

  31. 31.What is the perimeter of a regular hexagon with side 4?

  32. 32.A line through (0, 1) and (2, 5) is parallel to which line?

  33. 33.The point (4, −3) is reflected across the y-axis. What is the image?

  34. 34.A chord is 8 centimeters from the center of a circle of radius 10. How long is the chord?

  35. 35.What is the sum of the interior angles of a pentagon?

  36. 36.A student dilates a figure by a factor of 2 about the origin and says the area also doubles. What is the area factor?

  37. 37.What is the volume of a sphere with radius 3? Use the formula (4/3)πr^3.

  38. 38.A ladder 10 feet long reaches 8 feet up a wall. How far is the base of the ladder from the wall?

  39. 39.Two lines are perpendicular. One has slope 3. What is the slope of the other?

  40. 40.A triangle has sides 5, 5, and 6. Which statement is true?

  41. 41.Can sides 2, 3, and 6 form a triangle?

  42. 42.A parallelogram has base 9 and height 4. What is its area?

  43. 43.A trapezoid has bases 6 and 10 and height 4. What is its area?

  44. 44.A student measures the slant height of a cone and uses it as the height in the volume formula. What should the teacher ask?

  45. 45.What is the circumference of a circle with diameter 14? Leave π in the answer.

  46. 46.Point A is (1, 1) and point B is (4, 5). A student says the slope is 4/3. Is that the slope from A to B?

  47. 47.A circle has equation (x − 2)^2 + (y + 1)^2 = 9. What are the center and radius?

  48. 48.Vertical angles are formed by two intersecting lines. One angle is 115°. What is the angle opposite it?

  49. 49.A regular polygon has an exterior angle of 40°. How many sides does it have?

  50. 50.A student finds the area of a sector with a 60° central angle and radius 6 as (60/180)π(36). What is the area?

  51. 51.The diagonals of a rhombus are 6 and 8. What is the area of the rhombus?

  52. 52.A right triangle has opposite side 7 and adjacent side 24 for a given acute angle. What is tan of that angle?

  53. 53.A map uses a scale of 1 centimeter to 5 kilometers. A road is 3.2 centimeters on the map. How long is the road?

  54. 54.Which transformation preserves both lengths and angle measures but reverses orientation?

  55. 55.A rectangle has area 48 and width 6. What is its length?

  56. 56.A student says the volume of a cube doubles when the edge doubles. What is the volume factor?

  57. 57.What is the area of an equilateral triangle with side 2? Use (√3/4)s^2.

  58. 58.Two chords of a circle intersect inside the circle. One chord is divided into segments of 2 and 6. The other is divided into segments of 3 and which length?

  59. 59.A tangent and a radius meet at the point of tangency. What is the angle between them?

  60. 60.The points (0, 0), (4, 0), and (0, 3) are vertices of a triangle. What is its area?

  61. 61.A student labels the longer diagonal of a rectangle as a line of symmetry. Is a diagonal of a non-square rectangle a line of symmetry?

  62. 62.What is the length of the arc intercepted by a 60° central angle in a circle of radius 6? Leave π in the answer.

  63. 63.A triangle is rotated 180° about one vertex. Which properties stay the same?

  64. 64.The line y = 3 is which kind of line?

  65. 65.A student computes the area of a circle of diameter 10 as π(10)^2 = 100π. What feedback fits?

  66. 66.What is the distance from the point (0, 0) to the point (5, 12)?

  67. 67.A quadrilateral has exactly one pair of parallel sides. What is it?

  68. 68.A right circular cone has radius 3 and perpendicular height 4. What is the slant height?

  69. 69.Which set of points is collinear?

  70. 70.A teacher asks why the area of a triangle is half the area of a parallelogram with the same base and height. Which reply is sound?

  71. 71.What is the measure of each interior angle of a regular octagon?

  72. 72.A cylinder has volume 40π and height 10. What is the radius of the base?

  73. 73.A triangle has angles 90°, 45°, and 45°, and a hypotenuse of 10. What is each leg?

  74. 74.Which figure has rotational symmetry of 180° but not 90°?

  75. 75.The midsegment of a triangle joins the midpoints of two sides. If the third side is 14, how long is the midsegment?

  76. 76.A student says SAS means any two sides and any angle. Which case is not SAS?

  77. 77.What is the area of a regular hexagon made of 6 equilateral triangles of area 5 each?

  78. 78.A point is 5 units from the origin and lies on the positive x-axis. What are its coordinates?

  79. 79.A triangle has sides 7, 8, and 9. A student uses the Pythagorean theorem and says it is right. What should be checked?

  80. 80.What is the volume of a square pyramid with base side 6 and perpendicular height 5? Use (1/3) × base area × height.

  81. 81.Two similar figures have areas 4 and 36. What is the scale factor from the smaller to the larger?

  82. 82.A line segment from (1, 2) to (7, 2) is translated up 4 units. What is the image of the segment?

  83. 83.The supplement of a 28° angle is which measure?

  84. 84.A coordinate proof places a rectangle with vertices (0, 0), (6, 0), (6, 2), and (0, 2). What is the length of a diagonal?

  85. 85.A student finds the perimeter of a semicircle of radius 5 as π(5), the curved part only. What is the perimeter of the semicircular region, including the diameter?

  86. 86.Which pair of angles is always congruent when two parallel lines are cut by a transversal?

  87. 87.A cube has volume 64. What is the length of an edge?

  88. 88.A circle is inscribed in a square of side 10. What is the area of the circle?

  89. 89.A square is inscribed in a circle of radius 5, so the diagonal of the square is 10. What is the area of the square?

  90. 90.A student graphs y = x + 1 and y = x + 4 and says the lines meet at a large x-value. What is true?

  91. 91.The area of a triangle is 30 and the base is 12. What is the corresponding height?

  92. 92.Which statement about a parallelogram is always true?

  93. 93.A dilation about the origin with scale factor 1/2 sends (8, −4) to which point?

  94. 94.A right triangle has legs 9 and 12. A student says the hypotenuse is 15, then divides every side by 3 and says 3-4-5. Is that a similar triangle?

  95. 95.What is the lateral surface area of a cylinder with radius 2 and height 7, not counting the bases?

  96. 96.An angle in a triangle is 100°. What kind of triangle is it?

  97. 97.The equation x = −2 is which line?

  98. 98.A teacher shows two triangles with two pairs of congruent angles. What may the class conclude?

  99. 99.A rectangular room is 8 feet by 15 feet. How many square feet of carpet cover the floor?

  100. 100.A chord passes through the center of a circle. What is that chord called, and how does its length compare with other chords?

  101. 101.What is the midpoint of (−4, 6) and (2, −2)?

  102. 102.A student says the volume of a cone is πr^2 h. Which comparison corrects that?

  103. 103.Two angles of a triangle are congruent, and the third angle is 80°. What is each base angle?

  104. 104.A net of a cube is folded. How many square faces does the solid have?

  105. 105.The slope of the line through (2, 5) and (2, 9) is which value?

  106. 106.A design is reflected and then reflected again across the same line. What is the result?

  107. 107.A rectangular prism is 5 by 5 by 2. What is its surface area?

  108. 108.A class is asked which measurement changes when a figure is translated. Which answer should the teacher accept?