Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
History of trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Multilateration wikipedia , lookup
Line (geometry) wikipedia , lookup
Perceived visual angle wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
FIRST SEMESTER REVIEW NAME______________________________________DATE_________________PER.______ GEOMETRY FALL SEMESTER REVIEW PART 1. GEOMETRY BASICS Know the definitions of each of the following terms. Point Ray Line Midpoint Plane Coordinate Coplanar Points Collinear Points Line Segment Using the figure below, name each of the following. 1. ____________ 2. ____________ 3. ____________ The intersection of M and L L B C A ray opposite DB E D M A plane containing CE A 4. ____________ The intersection of L and CE Refer to the number line below to find the measures for problems 14 – 16. V WT -6 -5 -4 -3 -2 -1 Y RU ZX S 0 2 1 3 4 5 6 5. d = _______________ Find the distance between X and T. 6. d = _______________ What is the distance between Z and W? 7. _______________ What point(s) is/are two units from point U? Find the indicated value. 8. x = _______________ If A is between X and Y, and XA = 3x, AY = 2x + 5, and XY = 60, find the value of ‘x’. (Draw a picture…it helps!) 9. d = _______________ Find the distance between the points E(-3, -4) and F(5, 4). Simplify the radical if necessary. Refer to the number line to find the coordinate of the midpoint of each segment. A E -6 -5 -4 -3 -2 -1 10. m = _______________ AC 11. m = _______________ BD B 0 C D 1 2 3 4 5 6 Find the midpoint of the segment with the given endpoints. 12. m = _______________ (-3, 6) and (2, -8) Find the indicated length. 13. FG = _______________ F is the midpoint of EG. If EF = 2x + 3 and EG = 6x – 3, find FG. PART 2. ANGLE BASICS Using the figure below, find the indicated measures. A 14. mCED = __________ D mFEC = 32, find mCED. E 15. x = __________ mCEA = (6x – 20), mAED = (3x + 18), and mCED = 151. Find the value of ‘x’. C F Use the figure below to answer the following questions. 16. ____________________ Name a pair of adjacent, complementary angles. 17. ____________________ Which angle is vertical to STR? 18. ____________________ The measure of PTR is twice the measure of NTP. Find the measure of both angles. P N Q T M R S In the figure below, BA and BC are opposite rays, and BE bisects ABD. 19. mABE = __________ If mABE = (6x + 2) and mDBE = (8x – 14), then find mABE. 20. mEBD = __________ If mABE = (12n – 8) and mABD = (22n – 11), then find mEBD. Know the definition of each of the following terms. angle acute angle right angle midpoint vertex obtuse angle congruent angles complementary angles straight angle supplementary angles angle bisector vertical angles adjacent angles collinear segment bisector D E A B C Find the indicated measures. 21. ____________________ An angle’s measure is 43 less than 6 times the measure of its complement. Find the measure of both angles. 22. ____________________ Find the measures of two complementary angles, A & B, if mA = (7x + 4) and mB = (4x + 9). PART 3. PARALLEL LINES & TRANSVERSALS Use the figure below for problems 1. – 6. Identify each angle pair and tell whether they are congruent or supplementary. 23. TYPE:____________________ or or or 5 6 7 8 4 and 5 supplements? 25. TYPE:____________________ 1 2 3 4 supplements? 24. TYPE:____________________ 1 and 5 2 and 8 supplements? Find the value of ‘x’ in each of the following. (2x – 3) 26. x = ____________ 135 (2x + 7) 27. x = ____________ 103 SECOND SIX-WEEKS REVIEW PG. 2 Given l m, m1 = 98, and m2 = 40, find the measure of each angle. 28. _______________ 9 8 2 m4 = ? 1 29. _______________ 30. _______________ 4 l 7 b 3 m8 = ? m9 = ? 6 m 5 a Find the indicated value(s). 31. x = ____________ Find the values of ‘x’ and ‘y’. (3y + 8) (4x + 9) y = ____________ (19x + 10) Use the pyramid below to answer questions 16 and 17. M 32. _________________________ Name all pairs of parallel segments. 33. _________________________ Name a segment skew to AE. R D A E PART 4. ANGLES OF POLYGONS Answer each of the following questions. 34. m = ____________ Find the missing angle in LMN and classify the triangle by angles. L Classify: 35. m = ____________ Find the measure of angle T and classify the triangle by angles. Name the sides of LMN in order from smallest to largest. 37. Angles: Name the angles in MOT from largest to smallest. N 67 80 M Classify: 36. Sides: 10 7 5 75 T O 8 Determine whether it is possible to form a triangle with the given lengths of sides. If yes, classify the triangle by SIDES. 38. YES or NO 5, 4, and 3 NO 5, 10, and 15 Classify: 39. YES or Classify: Find the value of ‘x’ in each of the following. 40. x = ____________ (x + 10) x (x + 20) 41. x = ____________ (x – 37) (x – 42) x Find the indicated measure. 42. sum = ____________ Find the sum of the measures of the interior angles of an octagon. 43. each = ____________ Find the measure of each interior angle of a decagon. 44. sum = ____________ Find the sum of the measures of the exterior angles of a 20gon. 45. each = ____________ Find the measure of each exterior angle of a regular 15gon. PART 5. QUADRILATERALS Complete each statement about 46. Answer:____________ MARK and tell why you chose that answer. MKR ? Why? K 47. Answer:____________ AS ? R S Why? M 48. Answer:____________ Why? ARK and _____ are supplementary. A For each parallelogram, find the values of ‘x’, ‘y’, and ‘z’. 49. x = _______________ x y = _______________ y z z = _______________ 118 50. x = _______________ y y = _______________ z z = _______________ 20 x 42 Use rhombus RSTV and the given information to find each value. 51. ____________ If mRST = 67, find the mRSW. S T W 52. ____________ If mSWT = (2x + 8), find the value of ‘x’. R V Use rhombus ABCD and the given information to find each value. A 53. ____________ B If mACD = 34, find mABC. F 54. ____________ What is the value of ‘x’ if mBAC = (4x + 6) and mACD = (12x – 18)? D C WXYZ is an isosceles trapezoid with bases WZ and XY and median MN. Use the given information to solve each problem. 55. MN = ____________ Find MN if WZ = 11 and XY = 3. W M X 56. XY = ____________ If MN = 10 and WZ = 14, find XY. 57. x = ____________ If MN = 10x + 2, WZ = 21, and XY = 8x +19, find the value of ‘x’. Y N Z ABCD is an isosceles trapezoid. Decide whether each statement is TRUE or FALSE (circle one), and explain your reasoning. 58. TRUE or FALSE AC = BD Explain: B A 59. TRUE or FALSE AD CB D Explain: 60. TRUE or FALSE E C CA and BD bisect each other. Explain: Quadrilateral EFGH is a rectangle. Find the value of ‘x’. 61. x = ____________ mHEG = (12x + 1) and mGEF = (6x – 1) E H J 62. x = ____________ JF = 8x + 4 and EG = 24x – 8 F G