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| Table of Contents: 1. Basic Geometry ....... [BEO] 2. Polygons ............. [PEO] 3. Relations and Sizes .. [REO] 4. 3D Geometry .......... [3EO] 5. Greek Vocabulary ..... [GVO] 1. Basic Geometry [BEO] {Building Blocks} = {Point, Line, Plane, Space} Point; 0D, a location Line; 1D, consists of 2+ collinear points Plane; 2D, consists of 3+ noncollinear points at the same depth Space; 3d, consists of 3+ noncollinear points of different depth {Line} = {Line Segment, Ray, Line} Line Segment; 2 endpoints Ray ; 1 endpoint Line ; 0 endpoints {Line Pairs} = {Intersecting, Parallel, Perpendicular, Skew} Intersect ; Lines intersect Perpendicular; Lines intersect at a right angle Parallel ; Lines do not intersect and are on the same plane Skew ; Lines do not intersect and are on different planes {Angle} = {right, obtuse, acute, straight, interior}; two rays with the same vertex Right ; 90 Degrees Obtuse ; >90 Degrees Acute ; <90 Degrees Straight; 180 degrees Inscribed; Angle with vertex on edge of circle Interior; Angle with vertex inside circle Circle: Origin ; Center of the circle Chord ; A line segment across Diameter ; Chord across the origin Radius ; Distance from the origin Circumference; Distance around Arc ; A partition of the circumference Sector ; A wedge Tangent ; Line perpendicular to radius 2. Polygons [PEO] {Polygons} = {regular, equiangular, equilateral convex, concave} Equiangular; All angles congruent Equilateral; All sides congruent Regular ; Equiangular and equilateral Convex ; A stright line can only cross two sides Concave ; A straight line *can* cross more than two sides {Polygon Anatomy}= {Side, Vertex, Diagonal, Interior Angle Exterior Angle} Side ; A line segment composing the polygon Vertex ; Point where sides meet Diagonal ; A line connecting two vertices that isn't a side Interior Angle; Angle inside the polygon Exterior Angle; Angle external to the polygon Name |Sides|Angles|Verticles|Diagonals| Triangle | 3 | 3 | 3 | 3 | Quadrilateral| 4 | 4 | 4 | 2 | Pentagon | 5 | 5 | 5 | 5 | Hexagon | 6 | 6 | 6 | 9 | Heptagon | 7 | 7 | 7 | 14 | Octagon | 8 | 8 | 8 | 20 | Nanagon | 9 | 9 | 9 | 27 | Decagon | 10 | 10 | 10 | 35 | *Degrees(Angles) = (N-2)180d *Diagnols = N(N-3)/2 *Triangles = N-2 {Triangle} = {scalene, isosceles, equilateral ;acute, obtuse, right} Scalene ; No sides are equal Isosceles; Two sides are equal (equal sides, legs; odd side, base) Equilateral; All sides are equal (angles = 60d) (always acute) Acute ; All angles are acute Obtuse ; One angle is obtuse Right ; One angle is right {Quadrilateral} = {square, rectangle, parallelogram, trapezoid rhombus, kite} Parallelogram; Opposite sides parallel and congruent -Rectangle ; 4 right angles -Rhombus ; A parallelogram with four equal sides --Square ; Rectangle and Rhombus Trapezoid ; Only one pair of parallel lines Kite ; Two pairs of equal adjacent sides Area: Parallelogram; Base*Height Triangle ; Base*Height/2 Circle ; πr^2 Trapezoid ; (base1+base2)h/2 Ellipse ; π*r1*r2 3. Relations and Sizes [REO] Congruent; Exactly the same Similar; Same angles and sides in proportion Expondents; x^x -Squares; x^2 -Cubes ; x^3 Pythagreon Theorem; a^2 + b^2 = c^2 (for right triangles) A&B; Leg C; Hypotenuse 4. 3D Geometry [3EO] {3D} = {length, width, height} {Space Figure} = {polyhedron, cylinder, cone, sphere} Polyhedron; Bounded by plane polygons Cylinder; Tcongruent circular bases Cone ; One vertex and a circular base Sphere ; All points in space equidistant from the center {Polyhedron} = {prism, pyramid} Prism; Two parallel congruent bases & parallelogramical lateral faces Pyramid; Polygon base and triangle faces sharing vertex Volume: Prism ; Base*Height Pyramid; Base*Height/3 Cylinder; πr^2*Height Cone ; πr^2*Height/3 Sphere ; (πr^2)4/3 Ellipsoid; π(r1*r2*r3)4/3 Area: Prism ; (Circumbase)*height + 2(base area) Sphere ; 4πr^2 Cylinder; 2πr^2 + 2πr*height 5. Greek Vocabulary [GVO] 1 ; Un 2 ; Do 3 ; Tri 4 ; Tetra 5 ; Penta 6 ; Hexa 7 ; Hepta 8 ; Octa 9 ; Ennea 10 ; Deca 13 ; Tridecagon 19 ; Enneadecagon 20 ; Icosa 25 ; Icosikaipentagon 30 ; Trianconta 40 ; Tetraconta 50 ; Pentaconta 60 ; Hexaconta 70 ; Heptaconta 80 ; Octaconta 90 ; Enneaconta 100; Hecto 1000; Chilia 10000; Myria |