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Student Name: ___________________________ Date: ______ Per: ___________ Geometry Honors “Practice” Final Exam Problem Points Earned 1 ____ out of 3 2 ____ out of 4 3 ____ out of 3 4 ____ out of 9 5 ____ out of 2 6 ____ out of 2 7 ____ out of 8 8 ____ out of 6 9 ____ out of 6 10 ____ out of 5 11 ____ out of 3 12 ____ out of 5 13 ____ out of 6 14 ____ out of 8 Proof #1_____ ____ out of 10 Proof #2_____ ____ out of 10 Proof #3______ ____ out of 10 TOTAL ____ out of 100 1. 2. A square pyramid with a base edge of 4 inches, is inscribed in a cone with height of 6 inches. Find the volume of the cone in terms of . [4 points] 3. [3 points] 4. [9 points] 5. 6. [2 points] [2 points] 7. 8. (6 points) 9. [6 points] 10. Given: RST with medians ̅̅̅̅̅ ̅̅̅̅ RP = 2y – x, TP = 2y, PM = y – 2, and PN = x + 2 Find: The longer of the two medians. [5 points] 11. 12. [5 points] 13. Trapezoid TRAP, with median MQ, is shown in the diagram below. Solve algebraically for x and y and find the measure of MQ and measure of angle R. [6 points] x= y= MQ = m 14. A right cylindrical log is pictured below. [8 points] Part a: Calculate the exact volume of the cylindrical piece. Part b: Calculate the exact surface area of the cylindrical piece above. Part II: Proofs Choose 3 of the following 5 proofs. Each proof is worth 10 points. Mark which 3 proofs you want graded. 15. 16. 17. Draw a diagram, state what is given and the conclusion, and write the proof. If a point on the base of an isosceles triangle is equidistant from the midpoints of the legs, then that point is the midpoint of the base. 18. 19. Find the coordinates of the points that are equidistant from the lines whose equations are y = 3x - 2 and y = -3x - 4 and also three units from the intersection of the lines whose equations are y = x + 2 and y = -x . Round your answers to the nearest thousandths.