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NAME: _______________________________________ PERIOD: ________ DATE:_____________ GEOMETRY SEMESTER 1 REVIEW Use the diagram at the right for Exercises 1. 1. What is the intersection of the two planes? 2. bisects ABC so that mABD = 2y and mDBC = 5y – 12. What is mDBC? 3. ABC and CBD are supplementary angles. mABC = 8x + 12 and mCBD = 2x + 28. What is mABC? What is the mCBD? 4. Graph the figure in the coordinate plane and find the PERIMETER. Coordinate points are: L(0,1), M(3, 5), N(5,5), P(5,1). 1 5. QR has endpoints Q (9, 2) and R (3, 5). What are the coordinates of its midpoint X? 6. The midpoint of GH is (4, 7). One endpoint is H (12, 3). What are the coordinates of endpoint G? 7. Identify a pattern and find the next three numbers in the pattern. a. 5, 10, 20, 40, . . . b. 5, 8, 11, 14, . . . c. 3, 1, 1, 3, . . . d. 1, 3, 6, 10, 15, . . . 8. Determine if the conditional is true or false. If it is false, find a counterexample. a. If the figure has four congruent angles, then the figure is a square. b. If an animal barks, then it is a seal. 9. Write the converse, inverse, and contrapositive of the given conditional statement. a. If two angles are complementary, then their measures sum to 90. 2 b. If a figure is a rectangle, then it has exactly four sides. 10. Is each statement below a good definition? If not, explain. a. A rectangle is a quadrilateral with four congruent angles. b. A hexagon is a polygon with exactly six sides. 11. Decide whether the angles are alternate interior angles, same-side interior angles, corresponding angles, or alternate exterior angles. a. 2 and 7 b. 5 and 4 c. 8 and 3 d. 6 and 4 e. 1 and 5 12. Find the distance between each pair of points a. A(6, 7), B(1, 7) b. C(5, 5), D(5, 3) c. E(1, 0), F(12, 0) d. Q(2, 6), T(10, 0) 3 13. Circle the correct answer; show all work on a separate sheet of paper. Label problems on your separate sheet of paper 13.1 – 13.6. 14. Rewrite each equation in slope intercept form. Then determine whether the lines are parallel. Explain. a. 2y = x + 15 b. 10y + 130 = 50x c. 2y = 15 + 4x x = 2y + 5 5y = 2x + 11 6y 30 = 12x 4 15. Circle the correct answer; show all work on a separate sheet of paper. Label problems on your separate sheet of paper 15.1 – 15.6. 16. Given: mABC = 80 DBC = mABC Angle Addition Postulate Substitution Property (3x + 3) + (6x + 5) = 80 a. 9x + 8 = 80 b. 9x = 72 c. x=8 Angle Addition Postulate Substitution Property 5 17. Complete the two-column proof. Given: BD AB , BD DE , BC DC Prove: A E Statements Reasons 1) BD AB , BD DE 1) 2) CDE and CBA are right angles. 2) Definition of right angles 3) CDE CBA 3) 4) 4) Vertical angles are congruent. 5) BC DC 5) 6) 6) 7) A E 7) 18. CONSTRUCTION & Complete the two-column proof. Use a construction to prove that the two base angles of an isosceles triangle are congruent. Given: Isosceles ABC with base AC . Prove: A C Statements Reasons 1) ABC is isosceles. 1) 2) AB CD 2) Definition of isosceles triangle. 3) Construct the midpoint of AC and call it D. Construct DB . 4) 3) Construction 5) BD BD 5) 6) ABD CBD 6) 7) 7) 4) Definition of midpoint 6 19. Circle the correct answer; show all work on a separate sheet of paper. Label problems on your separate sheet of paper 19.1 – 19.6. 20. a. Find MN. b. Find MQ. c. Find MP. d. Find PS. 7 21. Find the value of x: 22. Find the value of x: 8 23. P is the centroid of MNO. MP = 14x + 8y. Write expressions to represent PR and MR. 24. F is the centroid of ACE. AD = 15x2 + 3y. Write expressions to represent AF and FD. 25. Circle the correct answer; show all work on a separate sheet of paper. Label problems on your separate sheet of paper 25.1 – 25.5. 9 26. Find the sum of the angle measures of each polygon. 27. Algebra Find the missing angle measures. 10 28. For what value of x is the figure the given special parallelogram? rhombus rectangle Use the diagram at the right for Exercises 7 and 8. 29. Two points that are 2 units from T. 30. A segment congruent to QT 11 31. Using the Law of Detachment, what conclusion, if any, can you make from the two given statements? Statement 1: If x = 3, then 3x – 4 = 5. Statement 2: x = 3 a. b. c. d. 3x – 4 = 5 x=3 If 3x – 4 = 5, then x = 3. not possible If possible, use the Law of Detachment to make a conclusion. If it is not possible to make a conclusion, tell why. 32. Using the Law of Detachment, what conclusion, if any, can you make from the two given statements? If a triangle is a right triangle, then the triangle has one 90º angle. ABC is a right triangle. If possible, use the Law of Syllogism to make a conclusion. If it is not possible to make a conclusion, tell why. 33. To take Calculus, you must first take Algebra 2. To take Algebra 2, you must first take Algebra 1. 34. A quadrilateral has four congruent sides if and only if it is a rhombus. A square is a rhombus. 12 35. Developing Proof Fill in the missing statements or reasons for the two-column proof. Given: E is the midpoint of DF . Prove: DE = 23 Statements Reasons 1) E is the midpoint of DF . 1) 2) 2) Definition of midpoint 3) 6x + 5 = 8x – 1 3) 4) 5 = 2x – 1 4) 5) 5) Addition Property of Equality 6) 7) DE = 6x + 5 8) DE = 6(3) + 5 9) DE = 23 6) Division Property of Equality 7) Given 8) 9) 36. Find the measure of each angle 1 and 2: 13 37. Use the map below to answer these questions: 14