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Geometry 1st Semester Review Name:________________________ 1. State the converse, inverse and contrapositive of the following statement: “If R is acute, then mR is less than 90.” Converse:_______________________________________________________________ Inverse:_________________________________________________________________ Contrapositive:___________________________________________________________ 2. What is the appropriate conjecture based on the given if…then statement? Given: If it is Monday, then tomorrow is Tuesday. It is Monday. 3. Find a counterexample for the following conjecture. x3 0 Conjecture: 4. Find the coordinates of M , the midpoint of AB . A(-2, 4) B(10, -6) a 5. If a // b, m1 4x 12 , and m2 9x 58 , find m1 . b 1 2 6. Find the mx . 35 x 25 7. The perimeter of FED is 53. By solving for x , determine whether FED is scalene, isosceles, or equilateral. F 17 x + 12 E 3x D 8. Which three lengths could form a triangle? Explain why. A. 6, 6, 15 ___________________________________________________________ B. 7, 10, 12___________________________________________________________ C. 8, 12, 20___________________________________________________________ 9. Given B D and BD bisects AE at C . By what method is ACB ECD ? D A C E B 10. Find the sum of the interior angles of a heptagon. 11. For lunch, Avery can choose either a hamburger (H) or a burrito (B) and either a soda (S) or water (W). What is the outcome set for the lunches he could get? 12. Determine whether each situation involves a permutation or a combination. A. 6 books selected from a group of 15. B. arrangement of 6 CD’s on a shelf. 13. Cami has 4 kinds of lettuce growing in her garden. How many different salads can she make using 2 of the types of lettuce? 14. How many different ways can 11 different candidates finish in first, second and third places in an election? 15. Which of the following algorithms are equivalent? I. Given two lines, draw a transversal. If the alternate interior angles are equal, then you have the answer you are looking for. II. Given two lines, compare their slopes. If they are equal, then you have the answer you are looking for. III. Given two lines, compare their slopes. If they are negative reciprocals, then you have the answer you are looking for. 16. In the figure, what point is collinear to F and J? I G H F J M L 17. In the diagram, name a pair of congruent angles. A D C E B 18. What is the complement of 37 ? What is the supplement of 37 ? Complement: Supplement: 19. Find the measure of ABC . C 3x + 5 A 7x + 25 B D 20. Given RST QST and RS QS . Which postulate can be used to prove that STR STQ ? S R T Q 21. Find the sum of the measures of the exterior angles of an octagon. 22. If AB 15 and AC 31, find BC . A B C 23. What symbol is used to indicate the following: A. two line segment are parallel _______________ B. two line segments a perpendicular___________ C. two line segments are congruent_____________ 24. What word describes an angle A. whose measure is greater than 0 and less than 90 _______________ B. whose measure is equal to 90 _______________ C. whose measure is greater than 90 and less than 180 _____________ D. whose measure is equal to 180 ______________ 25. Identify the hypothesis and conclusion of this conditional statement: “If two lines meet to form non-adjacent, non-overlapping angles, then they form vertical angles.” A. hypothesis: _______________________________________________________ _________________________________________________________________ B. conclusion: _____________________________________________________ _________________________________________________________________ 26. The measures of two angles of a triangle are 43 and 56. What is the measure of the third angle? 27. The measure of a base angle of an isosceles triangle is 57. What is the measure of the vertex angle? 28. Find the value of x. x 75 20 29. In TUV , mT 4x 6 , mU x 5 , and mV 3x 19 . List the angles from largest to smallest. 30. Choose the correct statement. A. m 1 < m 3 B. m 1 = m 3 C. m 1 > m 3 1 2 3 4 31. Define the following terms: A. Altitude __________________________________________________________ B. Median __________________________________________________________ C. Perpendicular bisector_______________________________________________ 32. If EIF FIG, then what is the best description of IF? E F G D I H 33. If mABD = 35 and mABC = 120, find mDBC. A D B C 34. Given SQ bisects RST. Find mQSR if mTSR = 72. T Q S R 35. Refer to the figure at the right to answer the following questions. A. Which two pairs of angles are same side interior angles? 1 B. Which two pairs of angles are alternate interior angles? 2 C. Which four pairs of angles are corresponding angles? 36. Given a // b. Find m4. a b 4 32 37. If a // b and m9 = 4x + 12 and m5 = 6x – 4, then find the value of x. a b 9 5 4 3 5 6 8 7 38. Given that TP KO and P O. Name one additional pair of corresponding parts that needs to be congruent in order to prove STP MKO by SAS. K T O M P S 39. Given ABC XYZ, AB = 17, YZ = 24, and XY = 7x – 4. Find the value of x. 40. List the properties of rectangles. 41. WXYZ is a rhombus. If XZ 15 , then find OZ . W X O Z Y 42. Given: parallelogram ABCD as marked. Find BC. A 12 D 9 B C 43. Fill in the blanks for the characteristics of a rhombus. A. The sides of the rhombus are ________________________. B. The diagonals of the rhombus are _____________________ and _____________. 44. Given parallelogram LOVE , mO 9x 15 and mE 4x 5 . Find mV . L O E V 45. If MATH is a square, find mMTH . M H A T 46. Fill in the blanks for the characteristics of an isosceles trapezoid. A. The diagonals are___________________________________________________ B. The bases are ______________________________________________________ C. The legs are _______________________________________________________ D. The base angles are _________________________________________________ 47. If ABCD is a trapezoid with bases of 6 and 12, what is the measure of its median? 48. Find the slope of a line passing through (-3, 7) and (5, -9). 49. Graph the line with a slope of 2 passing through point R 0, 5 . 50. What is the slope of the line perpendicular to a line with slope 4 ? 7