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MATH 205  This form is a review sheet for MATH 090 students based primarily around the  teaching & instructions of Professor V. Smith of ESU.  
Created by:  Jasmine E. Aue  [email protected] 
HELPFUL TIPS FOR COURSE CONTENT (ie. not formulas but important) 
Lines, Arrows, Points & Planes  This section is a review of lines, arrows, points & planes. How they are defined, look and  interact with each other.  
Collinear: same line  Coplanar: same plane  Closed: a line with an endpoint on each end, kind of like this   Half: a line with only one endpoint, kind of like this   Open: a line with no endpoints, like this   → → ↔=  
 
There is exactly one line containing any two distinct points  If two points are in a plane then the line of points are in a plane  If two planes intersect, there is a line at that intersection  There is exactly one plane that contains any 3 distinct 
 
   
 
 
Diameter of a Circle  
Formula 
| y is from (x,y), mxy = m + b  
is the slope, x is from (x,y) & b  is the y-intercept 
| this isy ) / (x )m = ( 2 − y1 2 − x1  
the point-slope formula, use  this to find the slope of a line  given two coordinate pairs  x , ) & (x , )( 1 y1 2 y2  
| Perimeter of a SquaresP = 4  
| Area of a SquareA = s2  
| Perimeter of aw lP = 2 + 2  
Rectangle 
| Circumferenced πrC = π = 2  
Triangle 
FE ABAY
Angles & Circles  This section is a review of angles and circles, not including their formulas (see formula list  for formulas). 
Complementary Angles: add to 90°  Supplementary Angles: add to 180°   Acute Angles: less than 90°  Right Angles: equal to 90°  Obtuse Angles: greater than 90° but less than 180°   Reflex Angles: greater than 180° but less than 360°  Straight Angles: equal to 180°   Circle: 360° 
(when going from degrees to minutes to1 360 ° 0 600"= 1 = 6 ′ = 3  
seconds, multiply & when going from seconds to minutes to  degrees, divide) 
Diagrams Related to Angles and Circles: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1 + b2  
1 2  
| Surface Area ofA B hS = 2 + P  
a Right Prism, where B = area  of the base and P =perimeter  of the base 
| Volume of a RighthV = B  
Prism 
Area of a Rectangular Prism 
| Volume of awhV = l  
Cube 
| Surface AreaA πrh πrS = 2 + 2 2  
of a Right Cylinder (regular  cylinder like a pringles can) 
| Volume of a Rightr hV = π 2  
Cylinder 
Sphere 
| Surface Area ofA P lS = B + 2 1  
a Pyramid (using slant height) 
|Volume of a PyramidV = 3 lwh  
| SurfaceA r rS = π √r2 + h2 + π 2  
Area of a Cone where √r2 + h2
is the slant height  
 
 
Interior Angles: 3, 4, 5, 6 Exterior Angles: 1, 2, 7, 8 Alternate Interior Angles: 3 & 6, 4 & 5 Alternate Exterior Angles: 1 & 8, 2 & 7 Corresponding Angles: 1 & 5, 2 & 6, 3 & 7, 4 & 8
d = a + b
Normal Distribution  This is a diagram of Normal Distribution: 
 
 
 
 
 
 
 
 
 
 
Shapes  This section is a review of shapes, triangles will have their own more detailed section  following this one. (see formula list for formulas on area, perimeter, volume, etc.) 
Simple: does NOT intersect itself  Closed: the start of the shape is also its end & vice versa.  Regular Polygon: equilateral (sides) & equiangular (angles)  Trapezoid: at least one pair of parallel lines  Kite: 2 pairs of adjacent & congruent angles  Parallelogram: Both pairs of opposite sides are parallel  Rhombus: two adjacent sides are congruent 
Diagrams Related to Shapes: 
STUDY TIPS 
Scheduling | keep up to date  with all assignments, quizzes,  tests, exams, etc. by  documenting them onto a  calendar you regularly check,  using a reminders app, a  planner or other scheduling  tool(s) 
Review | attend regular  tutoring sessions, create your  own mock tests using practice  problems, review past HW,  quizzes, tests & exams 
Eat Well |maintain a healthy,  balanced diet to increase  brain function (memory,  engagement, attention, etc.)  & to decrease fatigue,  fogginess, etc.  
Sleep Well | maintain a health  sleep schedule of 6-8 hours of  sleep per night 
TUTORING INFORMATION 
ESU’s WCOnline Tutoring  Link |    https://esu.mywconline.com 
 
every trapezoid is a quadrilateral .
EX .
NOT every rectangle is a quay.
Not every rhomboid is a rectangle .
Triangles  This section is a review of Triangles. (see formula list for formulas for area, perimeter, etc.) 
Diagrams Related to Triangles: 
 
Miscellaneous Information  This section is a review of miscellaneous information that does not fit a big enough  category to be a separate section. These concepts are just as important though! 
Area is always squared x )( 2  
Volume is always cubed x )( 3  
When going from to radians; °x °x • π 180°  
When going from radians to ; °x x • π 180°  
Kilo (1000), Hecto (100), Deka (10), GRAM (Base Measurement,  1),Deci (0.1), Centi (0.01), Milli (0.001) 
1 Ton = 1000000g = 1000kg  1kg = 1000g  1hg = 100g  1dkg = 10g  10dg = 1g  100cg = 1g  1000mg = 1g  cm mL g1 3 = 1 = 1  
dm L kg1 3 = 1 = 1  
yd 6in1 2 = 3 2  
1ft = 12in  1yd = 3ft = 36in  1mi = 1760yd = 5280ft = 63360in 
Vectors: 
GEOMETRY FINAL EXAM REVIEW
I. MATCHING _____reflexive A. a(b + c) = ab + ac _____transitive B. If a = b & b = c, then a = c. _____symmetric C. If D lies between A and B, then AD + DB = AB. _____substitution D. If a = b, then b = a. _____distributive E. a = a _____definition of midpoint F. If D is the midpoint of , then AD =
AB.
_____midpoint theorem G. If a + b = c and a = d, then d + b = c. _____segment addition postulate H. If D is the midpoint of , then AD = DB. II. Fill in the blank. 1. An equilateral triangle is also a(n) ___________triangle. 2. The ____________ is the longest side of a right triangle. 3. Similar triangles have congruent corresponding ____________ and the corresponding
__________ are in proportion. 4. In an isosceles triangle, the __________ angle is the angle that is different. 5. The __________ of a triangle is a segment from a vertex to the midpoint of the
opposite side. 6. A(n) ____________ of a triangle is a segment from a vertex A to the opposite side. 7. A(n) ____________ ____________ of a segment is a line, segment, or ray A to a
segment at its midpoint. 8. The measure of a central angle is _________ to its intercepted arc. 9. Two __________________ angles have a sum of 90q. 10. Two __________________ angles have a sum of 180q. 11. A __________ has only 1 endpoint. 12. If two lines are ____________, they form right angles. 13. Two lines intersect in a ____________. 14. Two planes intersect in a ____________. 15. Through any three collinear points there are ____________ ___________.
Through any three non-collinear points there is __________ ________ ________. 16. __________ angles measure between 0q and 90q. 17. __________ angles measure between 90q and 180q. 18. Find the side of square with area 16 units2. ____________. 19. If the ratio of the measures of the angles of a triangle is 2:2:5, then the triangle is a(n)
____________ triangle. 20. If 4 points all lie on the same line, then the points are ____________.
Name___________________
21. The interior angle sum of a hexagon is ____________. 22. The exterior angle sum of a decagon is ____________. 23. If each interior angle of a regular polygon is 144, then the polygon is a __________. 24. If each exterior angle of a regular polygon is 30, then the polygon has ____________
sides. 25. In a 30q - 60q - 90q triangle, the long leg is ______ times the short leg. 26. In a 45q - 45q - 90q triangle, the hypotenuse is ______ times the leg. 27. An angle inscribed in a semicircle is a __________ angle. 28. Write 32 in simplest radical form. ______ 29. If A is a right angle and mA = (4x + 10)°, then x = __________. 30. 3 & 5 are ____________ angles & therefore are ____________. 31. 4 & 5 are ____________ angles & therefore are ____________. 32. 2 & 6 are ____________ angles & therefore are ____________. 33. If m6 = (x + 5)° and m4 = (2x + 10)°, then m4 =______. 34. True or False. A triangle may have sides of 7, 12, and 18. 35. To find the area of a right triangle, the ____________ can be used as the base and
height. 36. is a ____________. 37. is a ____________. 38. is a ____________. 39. is a ____________. 40. is a ____________. 41. Point O is the _______________. 42. Point A is the _______________. 43. x = _____ 44. mABD = _____
1 2 a 3 4
5 6 b 7 8
a __ b
A B C
C D
45. x = _____ 46. B and E are the midpoints of AD and AG. If DG = 40, then CF _____. 47. Find the perimeter of a right triangle with legs 6 and 8. _____ 48. If the diagonals of a rhombus are 20 and 36, then the area is _____. 49. Find the area of a right triangle whose hypotenuse is 25 and whose leg is 7. _____ Name the theorem or postulate used to prove the triangles congruent. 50. __________ 51. __________ 52. __________ 53. __________
54. m = _____
55. m =_____ 56. mCOB = _____ 57. mAOB = _____ 58. Draw ACB. mACB = ______
4
8 9 x
m = 130q
35 37q
4 x°
XYZ is an equilateral triangle. 59. ZY = _____ 60. mZ = _____ 61. altitude = _____ 62. Area of Circle = _____ 63. Area of Square = _____ 64. Area of shaded region = _____ 65. Circumference of Circle = _____ 66. Perimeter of Square = _____ 67. Area of parallelogram = _____ Round your answer to the nearest whole number or degree. 68. Find x | ___________. 69. Find y | _____________ 70. A ladder is positioned against a house at a 65q angle. The ladder is 10 feet tall. How far away from the house is the base of the ladder? Round your answer to the nearest tenth. 71. x = _____ 72. y = _____ 73. z = _____
X 8ft Y
X ZY
74. x = _____
75. 2 tangent lines drawn to a circle from the same point are __________. 76. If the diagonals of a quadrilateral are A, then the quad. is a ______ or a ________. 77. If the diagonals of a quad. are A and #, then the quad. is a ____________. 78. If the diagonals of a quad. are #, then the quad. is a ____________ or a ___________. 79. The legs of an isosceles trapezoid are 10 ft. and the bases are 10 ft. and 22 ft. The length of the median is _____. The area of the trapezoid is ___________. 80. In a parallelogram, ______ angles are supplementary and _______ angles are congruent.
81. Given XYZ # RSN, then Y # _____ and _____
XZ # _____. 82. x = _____
83. m = 100q, m = 90q, mX = _____
84. is a __________ arc.
85. is a __________ arc. 86. Find the volume of a rectangular prism with length 6 in, width 3 in, and height 4 in. 87. Find the total (surface) area of a cylinder with radius 4 m and height of 3 m. 88. The total (surface) area of a cylinder is 66π cm2 and the radius is 3 cm. Find the volume. 89. What is the volume of a cone whose radius is 9 and slant height is 13? 90. The total (surface) area of a sphere is 64S . Find the radius of the sphere.
6 4
XZ and _____
WV . Prove: W # V 93. List the sides from largest to smallest. 94. Points A, B, and C are collinear. If AC = 8, BC = 6, and AB = 14, which point is in between the other two? ________________ 95. OA = 8 and mAOB = 90. Find AB. 96. In O, the radius is 41, and XZ = 18, find OM. 97. Find the scale factor of two rectangles if the perimeters are 36 cm and 48 cm respectively.
A
D
E
X
Y
Z
98. Name the transformation. 99. Name the transformation that maps ABC to ADE. 100. Two similar polygons are shown. Find the scale factor and the value of x. 101. YZ = √ and XZ = √ . Find XY. Answer in simplified radical form. 102. Describe the triangle with sides of 8, 2√ , 9. 103. If the hypotenuse in an isosceles right triangle measures 6√ ft., then the length of each leg is ________. 104. Find the volume of a square pyramid with base edge 5 in. and height 3 in.
Answers Matching E, B, D, G, A, H, F, C Fill in the Blank
1) Equiangular 2) Hypotenuse 3) Angles; sides 4) Vertex 5) Median 6) Altitude 7) Bisector 8) Equal 9) Complementary 10) Supplementary 11) Ray 12) Perpendicular 13) Point 14) Line 15) Infinite Planes;
Exactly One Plane 16) Acute 17) Obtuse 18) 4 units 19) Isosceles 20) Collinear 21) 720° 22) 360° 23) Decagon 24) 12 25) √ 26) √ 27) Right 28) √ 29) 20 30) Same Side Int.;
Supplementary 31) Alt Int;
Congruent 33) 120° 34) True 35) Legs
36) Radius 37) Diameter 38) Chord 39) Secant 40) Tangent 41) Center 42) Point of Tangency 43) 20 44) 70° 45) 6 46) 30 47) 24 units 48) 360 units2 49) 84 units2 50) SAS 51) ASA 52) HL or AAS 53) SSS 54) 50° 55) 50° 56) 50° 57) 180° 58) 90° 59) 8 60) 60° 61) √ 62) 25π units2 63) 100 units2 64) (100 – 25π) units2 65) 10π units 66) 40 units 67) √ units2 68) 57° 69) 28 70) 4.2 ft. 71) 75° 72) 75° 73) 30° 74) 3 75) Congruent 76) Rhombus; square 77) Square 78) Rectangle; Square
79) 15 ft. and 128 ft2 80) Consecutive;
Opposite 81) S; 82) 70° 83) 35° 84) Minor 85) Major 86) 72 units3 87) 56π units2 88) 72π cm3 89) 54π√ units3 90) 4 91) 75° 92) Y is the midpoint
of and (Given), (Def of Midpoint),
(Vertical Angles are Congruent), (SAS), (CPCTC)
93) 94) C 95) 8√ 96) 40 97)
98) Reflection 99) Dilation 100)
and x =
101) √ 102) Obtuse 103) 6 ft. 104) 25 in3
If you would like detailed answers please visit an MQC tutor (Tutoring Department contact information on
pg. 3)

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