Praxis Mathematics 5165 Domain 3: Geometry Welcome to your Praxis Mathematics 5165 Domain 3: Geometry 1. Praxis Mathematics (5165): Geometry In a triangle, if two angles measure \( 35^\circ \) and \( 55^\circ \), what is the measure of the third angle? A. \( 85^\circ \) B. \( 90^\circ \) C. \( 95^\circ \) D. \( 100^\circ \) None 2. Praxis Mathematics (5165): Geometry What is the area of a trapezoid with bases of lengths 8 cm and 14 cm and a height of 6 cm? A. \( 66 \text{ cm}^2 \) B. \( 72 \text{ cm}^2 \) C. \( 78 \text{ cm}^2 \) D. \( 84 \text{ cm}^2 \) None 3. Praxis Mathematics (5165): Geometry If two circles are tangent internally at point P, and the diameters of the circles are 10 cm and 6 cm, what is the distance from P to the center of the larger circle? A. 2 cm B. 3 cm C. 4 cm D. 5 cm None 4. Praxis Mathematics (5165): Geometry A regular hexagon is inscribed in a circle. If the radius of the circle is 8 cm, what is the perimeter of the hexagon? A. 24 cm B. 36 cm C. 48 cm D. 60 cm None 5. Praxis Mathematics (5165): Geometry What is the volume of a cylinder with a radius of 3 cm and a height of 10 cm? A. \( 90 \pi \text{ cm}^3 \) B. \( 100 \pi \text{ cm}^3 \) C. \( 270 \pi \text{ cm}^3 \) D. \( 300 \pi \text{ cm}^3 \) None 6. Praxis Mathematics (5165): Geometry A square and a regular hexagon have the same perimeter. If the side of the square is 6 cm, what is the length of each side of the hexagon? A. 2 cm B. 3 cm C. 4 cm D. 6 cm None 7. Praxis Mathematics (5165): Geometry In a 45-45-90 right triangle, if the length of one of the legs is \( \sqrt{2} \) units, what is the length of the hypotenuse? A. 1 unit B. 2 units C. \( \sqrt{2} \) units D. \( 2\sqrt{2} \) units None 8. Praxis Mathematics (5165): Geometry What is the sum of the interior angles of a polygon with 12 sides? A. \( 1440^\circ \) B. \( 1620^\circ \) C. \( 1800^\circ \) D. \( 1980^\circ \) None 9. Praxis Mathematics (5165): Geometry A cone has a height of 9 cm and a base radius of 3 cm. What is its slant height? A. 6 cm B. 9 cm C. \( \sqrt{90} \) cm D. \( \sqrt{81} \) cm None 10. Praxis Mathematics (5165): Geometry In a right triangle, if one angle measures \( 30^\circ \), what is the ratio of the length of the side opposite the \( 30^\circ \) angle to the hypotenuse? A. 1:02 B. 1:\(\sqrt{3}\) C. \(\sqrt{3}\):2 D. 2:\(\sqrt{3}\) None 11. Praxis Mathematics (5165): Geometry A sphere has a volume of \( 288\pi \text{ cm}^3 \). What is its surface area? A. \( 96\pi \text{ cm}^2 \) B. \( 144\pi \text{ cm}^2 \) C. \( 192\pi \text{ cm}^2 \) D. \( 288\pi \text{ cm}^2 \) None 12. Praxis Mathematics (5165): Geometry In an isosceles triangle, the base angles are each \( 45^\circ \). What is the measure of the vertex angle? A. \( 45^\circ \) B. \( 90^\circ \) C. \( 135^\circ \) D. \( 180^\circ \) None 13. Praxis Mathematics (5165): Geometry What is the length of the diagonal of a square with a side length of \( 5 \) units? A. \( 5\sqrt{2} \) units B. \( 10 \) units C. \( 25 \) units D. \( 5\sqrt{5} \) units None 14. Praxis Mathematics (5165): Geometry If a parallelogram has two consecutive sides of lengths \( 8 \) cm and \( 6 \) cm, and the angle between them is \( 60^\circ \), what is its area? A. \( 24 \text{ cm}^2 \) B. \( 48 \text{ cm}^2 \) C. \( 72 \text{ cm}^2 \) D. \( 96 \text{ cm}^2 \) None 15. Praxis Mathematics (5165): Geometry What is the radius of a circle inscribed in a triangle with sides \( 6 \) cm, \( 8 \) cm, and \( 10 \) cm? A. \( 1 \) cm B. \( 2 \) cm C. \( 3 \) cm D. \( 4 \) cm None 16. Praxis Mathematics (5165): Geometry A cube has a total surface area of \( 54 \text{ cm}^2 \). What is the length of one edge of the cube? A. \( 2 \) cm B. \( 3 \) cm C. \( 9 \) cm D. \( 27 \) cm None 17. Praxis Mathematics (5165): Geometry What is the sum of the exterior angles of any polygon, one at each vertex? A. \( 90^\circ \) B. \( 180^\circ \) C. \( 360^\circ \) D. \( 720^\circ \) None 18. Praxis Mathematics (5165): Geometry A right circular cone has a slant height of \( 10 \) cm and a radius of \( 6 \) cm. What is its lateral surface area? A. \( 30\pi \text{ cm}^2 \) B. \( 60\pi \text{ cm}^2 \) C. \( 120\pi \text{ cm}^2 \) D. \( 180\pi \text{ cm}^2 \) None 19. Praxis Mathematics (5165): Geometry The diagonals of a rhombus are \( 10 \) cm and \( 24 \) cm. What is the area of the rhombus? A. \( 60 \text{ cm}^2 \) B. \( 120 \text{ cm}^2 \) C. \( 240 \text{ cm}^2 \) D. \( 480 \text{ cm}^2 \) None 20. Praxis Mathematics (5165): Geometry An equilateral triangle has a side length of \( 12 \) cm. What is the radius of the circumscribed circle? A. \( 4\sqrt{3} \) cm B. \( 6\sqrt{3} \) cm C. \( 8\sqrt{3} \) cm D. \( 12\sqrt{3} \) cm None 1 out of 20 Time is Up! Time's up
