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Transcript
GPS Geometry Final Exam Review Unit 1 – Geometry Gallery Name: Multiple Choice (2 points each) Choose the best answer. 1. Find LP. [Note: Figure not drawn to scale] (A) LP = 4 L M (B) LP = 5 P (C) LP = 10 4 (D) LP = 8 6 5 N O 2. Opposite angles of a parallelogram are _________________. (A) Sometimes congruent (B) Always congruent (C) Complementary (D) Supplementary 3. Given square MNOP. The perimeter of MNOP is 72cm, NO = 2x + 6. Find x. (A) x = 15 (B) x = 12 (C) x = 9 (D) x = 6 4. Complete the congruence statement GJH ___ by ____. (A) GJH IJH by SAS (B) GJH IHJ by SAS (C) GJH IJH by HL J (D) GJH IHJ by HL I G H 5. The sides of a triangle are 12, 7 and x. Which of the following is a possible value for x? (A) 19 (B) 5 (C) 8 (D) 21 6. E is the midpoint of AC and BD . Choose the true statement. (A) AEB DEC by ASA A (B) AEB DEC by SAS (C) AEB CED by ASA E B D (D) AEB CED by SAS C 7. Given Q V and the figure shown, which statement is NOT necessarily true? (A) QAM VWM (B) QWA VAW (C) QAM VMW (D) WAM is isosceles V Q M A W (C) circumcenter (D) centroid 8. The medians of a triangle concur at the (A) orthocenter (B) incenter 9. Which points of concurrency may lie outside the triangle? (A) orthocenter and the circumcenter (B) circumcenter and incenter (C) centroid and incenter (D) centroid and orthocenter 10. In CAT , C is 54 and T is 36. What is the longest side of the triangle? (A) CA (C) CT (B) AT (D) cannot be determined Free Response Answer completely. 11. Given the diagram as shown, list the segments, AB, BC, AC, DC, and BD , in order of size starting with the smallest. A B 30 D C 12. Use the information in the diagram to solve for x. Show your work. 13. The diagonals of a quadrilateral are perpendicular to each other, what kind(s) of quadrilateral do we have? 14. In a certain regular polygon, the measure of an interior angle is equal to the measure of an exterior angle. How many sides does the polygon have? 15. Find the value of each variable in the parallelogram. 16. Write the contrapositive of the following statement. “If we go to bed late, then we will not pass the test.” 17. Given: JL KP , JL || KP Prove: JLK PKL 18. Postulate: If two lines are cut by a transversal so that corresponding angles are congruent then the lines are parallel. Theorem: If parallel lines are cut by a transversal then the alternate interior angles are congruent. a. State the converse of the theorem. b. Prove the converse of the theorem. a 1 2 3 b 19. Given the diagram below with GE, GD and GF are perpendicular bisectors of the sides of the triangle. C G F A D E B a. G is the ____________________ of the triangle. b. ABC is an obtuse triangle. How do you know this from the diagram without measuring the angles? c. If G is on ABC what kind of triangle would it be? Higher-level Standardized Test Questions (4 points each) 20. Given the diagram below. mD = 3x + 4, find x (A) x = 80 (B) x = 22 (C) x = 66 (D) x = 106 3 21. Given the diagram below, find mE. (A) mE = 130 (B) mE = 65 (C) mE = 50 (D) mE = 115 22. Which is the inverse of the following statement? “If it is Thursday, then we eat pizza.” (A) If we do not eat pizza, then it is not Thursday. (B) If we eat pizza, then it is Thursday. (C) If it is not Thursday, then we do not eat pizza. (D) If it is not Thursday, then we eat lasagna. 23. Which is a counterexample for the following statement? “If it grows, then it is alive.” (A) A dead tree (B) The national debt (C) A baby boy (D) A blue whale 24. Given the diagram at right, which theorem or postulate proves 3 7? (A) Congruent Complements Theorem (B) Side-Angle-Side Postulate (C) Vertical Angles Theorem (D) Corresponding Angles Postulate Solutions: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. B B D A C D C D A C DC, BD, BC, AB, AC x=14 kite, rhombus, square 4 b=90, c=80, d=100 If we pass the test, then we did not go to bed late. JLK PKL KL LK JLK PKL Alternate Interior Angles Theorem Reflexive Property SAS 18. a) If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. b) Given: 2 3 ; Prove: a b 2 3 2 1 1 3 a b Given Vertical Angles Theorem Transitive Property of Congruence Postulate 19. a) circumcenter b) the circumcenter is outside the triangle c) a right triangle 20. 21. 22. 23. 24. B D C B C