Created by: Jasmine E. Aue MATH 205 [email protected] This form is a review sheet for MATH 090 students based primarily around the teaching & instructions of Professor V. Smith of ESU. HELPFUL TIPS FOR COURSE CONTENT (​ie. not formulas but important​) FORMULA LIST ℉ = ((℃/5)(9)) + 32 | Lines, Arrows, Points & Planes Fahrenheit to Celsius formula This section is a review of lines, arrows, points & planes. How they are defined, look and interact with each other. ℃ = ((℉ − 32)/9)(5) ​ |​ Celsius to ❏ Collinear​: same line Fahrenheit formula ❏ 2 Coplanar​: same plane a2 + b = c2 |​ Pythagorean ❏ ● ● Closed​: a line with an endpoint on each end, kind of like this Theorem ❏ Half​: a line with only one endpoint, kind of like this ● d = (x − x ) + (y − y ) ❏ Open​: a line with no endpoints, like this √ 2 1 2 1 | ❏ → ⋃ → = ↔ Diameter of a Circle ❏ → ⋂ → = r2 = (x − h)2 + (y − k)2 |​ Radius ❏ ●● ⋃ ●→ = → Formula ❏ FE￮ ⋂ ￮ ￮ ￮ → → = a2 + b2 = c2 |​ Pythagorean ❏ Intersecting Lines​: lines that have only one point in common ❏ Intersecting Planes​: planes that have only one line in common Theorem ❏ Skew​: cannot be coplanar y = mx + b ​ |​ y is from (x,y), m ❏ Concurrent​: 3 or more intersections at the same point is the slope, x is from (x,y) & b ❏ Parallel​: same slope, non-intersecting is the y-intercept m = (y2 − y1) / (x2 − x1) |​ this is ❏ There is exactly one line containing any two distinct points the point-slope formula, use ❏ If two points are in a plane then the line of points are in a plane this to find the slope of a line ❏ If two planes intersect, there is a line at that intersection given two coordinate pairs ❏ There is exactly one plane that contains any 3 distinct (x1, y1) & (x2, y2) noncollinear points P = 4s ​ |​ Perimeter of a Square ❏ Collinear points/lines can have infinitely many planes 2 ❏ One line + one point = a unique line A = s ​ |​ Area of a Square ❏ Parallel lines are on one plane P = 2w + 2l ​ |​ Perimeter of a ❏ Two intersecting lines are on one plane Rectangle A = lw ​ |​ Area of a rectangle C = πd = 2πr ​ |​ Circumference of a Circle A = πr2 ​ |​ Area of a Circle P = a + b + c ​ |​ Perimeter of a Triangle A = 1 bh ​ |​ Area of a Triangle ABAY 2 Angles & Circles A = bh ​ |​ Area of a This section is a review of angles and circles, not including their formulas (​see formula list for formulas​). Parallelogram ❏ Complementary Angles: add to 90° 1 A = 2 (b1 + b2)h ​ |​ Area of a ❏ Supplementary Angles: add to 180° Trapezoid ❏ Acute Angles: less than 90° A = 1 d d ​ |​ Area of a Diamond ❏ Right Angles: equal to 90° 2 1 2 ❏ Obtuse Angles: greater than 90° but less than 180° SA = 2B + P h ​ |​ Surface Area of ❏ Reflex Angles: greater than 180° but less than 360° a Right Prism, where B = area ❏ Straight Angles: equal to 180° of the base and P =perimeter ❏ Circle: 360° of the base ❏ 1 360 = 1° = 60′ = 3600" (when going from degrees to minutes to V = Bh ​ |​ Volume of a Right seconds, multiply & when going from seconds to minutes to Prism degrees, divide) SA = 2lh + 2wh + 2lw ​ |​ Surface Diagrams Related to Angles and Circles: l Area of a Rectangular Prism V = lwh ​ |​ Volume of a Rectangular Prism 2 SA = 6s ​ |​ Surface Area of a me Cube V = s3 ​ |​ Volume of a Cube SA = 2πrh + 2πr2 ​ |​ Surface Area of a Right Cylinder (regular cylinder like a pringles can) N V = πr2h ​ |​ Volume of a Right Cylinder 2 SA = 4πr ​ |​Surface Area of a Interior Angles: 3, 4, 5, 6 Sphere Exterior Angles: 1, 2, 7, 8 4 2 V = 3 πr ​ |​ Volume of a Sphere Alternate Interior Angles: 3 & 6, 4 & 5 SA = B + 1 P l ​ |​ Surface Area of Alternate Exterior Angles: 1 & 8, 2 & 7 2 Corresponding Angles: 1 & 5, 2 & 6, 3 & 7, 4 & 8 a Pyramid (using slant height) lwh V = 3 ​ |​Volume of a Pyramid WHN Arc Minor 2 SA = πr√r2 + h + πr2 ​ |​ Surface I the transversal 2 2 l is Chord Area of a Cone where √r + h is the slant height \ 1 2 V = 3 πr h ​ |​ Volume of a Cone r Center Arc Major K(O,r) Radius d = a + b Circle “name” Normal Distribution This is a diagram of Normal Distribution: 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 Shapes problems, review past HW, quizzes, tests & exams 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.​) Eat Well |​maintain a healthy, ❏ Simple​: does NOT intersect itself balanced diet to increase ❏ Closed​: the start of the shape is also its end & vice versa. brain function (memory, ❏ Regular Polygon​: equilateral (sides) & equiangular (angles) engagement, attention, etc.) ❏ Trapezoid​: at least one pair of parallel lines & to decrease fatigue, ❏ Kite​: 2 pairs of adjacent & congruent angles fogginess, etc. ❏ Parallelogram​: Both pairs of opposite sides are parallel ❏ Rhombus​: two adjacent sides are congruent Sleep Well |​ maintain a health sleep schedule of 6-8 hours of Diagrams Related to Shapes: sleep per night TUTORING INFORMATION .. ... ESU Tutoring Website | https://www.esu.edu/tutoring g. /index.cfm ESU’s WCOnline Tutoring Link | https://esu.mywconline.com " - " / i I wearE T Ex . every quay is a rectangle . every trapezoid is a quadrilateral . NOT is a . EX . every rectangle 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: Special 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 (x2) ❏ Volume is always cubed (x3) π ❏ When going from x° to radians; x° • 180° 180° ❏ When going from radians to x° ; x • π ❏ 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 ❏ 1cm3 = 1mL = 1g ❏ 1dm3 = 1L = 1kg ❏ 1yd2 = 36in2 ❏ 1ft = 12in ❏ 1yd = 3ft = 36in ❏ 1mi = 1760yd = 5280ft = 63360in Vectors: iBBq Name___________________ 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 ^ to the opposite side. 7. A(n) ____________ ____________ of a segment is a line, segment, or ray ^ 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 90è. 10. Two __________________ angles have a sum of 180è. 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 0è and 90è. 17. __________ angles measure between 90è and 180è. 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 ____________. 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 30è - 60è - 90è triangle, the long leg is ______ times the short leg. 26. In a 45è - 45è - 90è 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 Ø A is a right angle and m Ø A = (4x + 10)°, then x = __________. 1 2 a 3 4 a || b 5 6 b 7 8 30. Ø 3 & Ø 5 are ____________ angles & therefore are ____________. 31. Ø 4 & Ø 5 are ____________ angles & therefore are ____________. 32. Ø 2 & Ø 6 are ____________ angles & therefore are ____________. 33. If m Ø 6 = (x + 5)° and m Ø 4 = (2x + 10)°, then m Ø 4 =______.