The truth is not hidden In the world of shapes, there exists simple truths.  From every angle, there are rules.  These rul...
Geometry is the study of figures. <ul><li>Plane geometry studies figures in a flat, two dimensional space called a plane. ...
1. POINTS  <ul><li>2.LINES AND THE ANGLESTHEY FORM </li></ul><ul><li>3. )INTERSECTING LINES AND  RULES ABOUT ANGLES FORMED...
INTERSECTING/PARALLEL  ANGLE DEFINED ANGLE RELATIONSHIPS Intersecting lines 3 WAYS TO DESCRIBE AN ANGLE Angle relationship...
Polygons:  plane closed figure made up of straight line segments. Remember type is defined by number of sides…3/triangle, ...
Angles equal/sides proportional vs. angles equal but sides same size and shape equal but sides same size and shape Similar...
Circles  :  a plane closed figure formed by a set of points equidistant from a fixed point called the center. <ul><li>Impo...
Coordinate Geometry <ul><li>Locates geometric figures on planes via Cartesian Coordinate System. If only x and y then it i...
Volumes on Volumes <ul><li>Shape </li></ul><ul><li>Cubes </li></ul><ul><li>Cylinders </li></ul><ul><li>Pyramids </li></ul>...
NOW THE TRUTH <ul><li>HAS  </li></ul><ul><li>TOTALLY </li></ul><ul><li>BEEN </li></ul><ul><li>REVEALED.  IF YOU MISSED IT,...
 
 
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  • GRE Tutor,GMAT Tutor,SAT Tutor,Statistics Tutor,Calculus Tutor,Precalculus Tutor,Algebra Tutor,Math Tutor,IB Tutor,AP Chemistry Tutor,AP Physics Tutor,MCAT Tutor,DAT Tutor,Statistics help,Math help,Chemistry help,Statistics Homework help,IB Chemistry Tuto

    1. 1. The truth is not hidden In the world of shapes, there exists simple truths. From every angle, there are rules. These rules, if followed, will bring you correct answers & great happiness. In math, all secrets are revealed.
    2. 2. Geometry is the study of figures. <ul><li>Plane geometry studies figures in a flat, two dimensional space called a plane. </li></ul><ul><li>Points, lines, and angles </li></ul><ul><li>Polygons-Triangles, Quadrilaterals…. </li></ul><ul><li>Perimeter and area </li></ul><ul><li>Circles </li></ul><ul><li>Solid geometry studies figures in a three-dimensional space. </li></ul><ul><li>Coordinate Geometry </li></ul><ul><li>Volume </li></ul>
    3. 3. 1. POINTS <ul><li>2.LINES AND THE ANGLESTHEY FORM </li></ul><ul><li>3. )INTERSECTING LINES AND RULES ABOUT ANGLES FORMED </li></ul>A LINE IS a continuous set of points having 1 dimension_length. A POINT has no dimension and only position. A LINE SEGMENT IS a part of a line ANGLE DEFINED: space formed when two lines meet at a point, Parallel lines ANGLE RELATIONSHIPS (adjacent/complementary) Intersecting lines (vertical/supplementary angles) 3 WAYS TO DESCRIBE AN ANGLE
    4. 4. INTERSECTING/PARALLEL ANGLE DEFINED ANGLE RELATIONSHIPS Intersecting lines 3 WAYS TO DESCRIBE AN ANGLE Angle relationships for intersecting lines Angle relationships for parallel lines 1) Angles opposite Each Other Are Equal and Called Vertical Angles Corresponding Angles Defined 2) Angles Adjacent to Each Other Are Supplementary Parallel lines defined Perpendicular Lines Intersect Ar Right Angles Alternate Interior Angles formed by transverse lines.
    5. 5. Polygons: plane closed figure made up of straight line segments. Remember type is defined by number of sides…3/triangle, 4/quadrilateral, 5/pentagon, 6/hexegon… Differences Shared Principles Similar verses Congruent: Angles equal/sides proportional vs. angles equal but sides same size and shape Sum of the Angles= (N-2) X 180 Each angle is #/N (because number of sides=number of angles.)
    6. 6. Angles equal/sides proportional vs. angles equal but sides same size and shape equal but sides same size and shape Similar vs. Congruent Polygons Sum of Angles: Triangle is 180 (3 types of triangles based on size of their sides are scalene (0=), isosceles(2=) and equilateral (3=), but based on their angles 3 classifications are acute (all angles less than 90 degree angles), right (1 90 degree) and obtuse (an angle greater than 90 degrees). Base angles, legs and vertex angles in Acute and Obtuse…legs and hypotenuse in right triangles. Quadrilateral is 360 The pythagorean triple: Any whole numbers, x, y, z whiich are the sides of a right triangle form x squared + y squared= z squared Learn common triples: 3, 4, 5 5, 12, 13, 8, 15, 17 Remember : Multiples of the x, y and z should be noted for speed! All triangles have the longest side opposite the greatest angle. The sum of the lengths of any two sides of triangles is greater than the third.
    7. 7. Circles : a plane closed figure formed by a set of points equidistant from a fixed point called the center. <ul><li>Important terms </li></ul><ul><li>Circumference: boundary </li></ul><ul><li>Radius: distance from center to any point on circumference. </li></ul><ul><li>Diameter-line segment passing through the center and ending on both ends at circ. </li></ul><ul><li>Chord: line segment having both endpoints on circ….longest one is diameter </li></ul><ul><li>Secant: line passing throught the circle interesting it at 2 points </li></ul><ul><li>Tangent: line intersecting the circle at only one point. Radius from that point is perpendicular to the tangent. </li></ul><ul><li>Arc: a part of the circ. </li></ul><ul><li>Semi-Cirlce- an arc that is ½ the circumference. </li></ul><ul><li>Sector: The interior part of circle boredered by two radiii and the arc they intercept. </li></ul><ul><li>Central Angle: verses inscribed angle…center point vs. point on circumference. </li></ul><ul><li>What is pi? Ratio Circ: diameterr of a circle! So pi X diameter=circ </li></ul><ul><li>The area of a circle: </li></ul><ul><li>A= pi r squared </li></ul><ul><li>Pi= 3.14 or 3.1 </li></ul><ul><li>or </li></ul><ul><li>3 1/7 or 22/7 </li></ul>
    8. 8. Coordinate Geometry <ul><li>Locates geometric figures on planes via Cartesian Coordinate System. If only x and y then it is two dimensions. If x, y and z then it is no longer on a plane but in space, so it is three dimensional. With x and y only, then two planes are divided into 4 quadrants. (I, 11, 111 and 1V) </li></ul><ul><li>Distance Sq.: (x2-x1)squared + (y1-y2)squared </li></ul><ul><li>So the square root of the dist= square root of above </li></ul><ul><li>Midpoint x1 + x2 /2, y1+y2/2= x midp..y midp. </li></ul><ul><li>Slope: m = y2-y1/X2 - X1 </li></ul>
    9. 9. Volumes on Volumes <ul><li>Shape </li></ul><ul><li>Cubes </li></ul><ul><li>Cylinders </li></ul><ul><li>Pyramids </li></ul><ul><li>Cones </li></ul><ul><li>Sphere </li></ul><ul><li>Formula </li></ul><ul><li>V= e cubed </li></ul><ul><li>V=pi r squared h </li></ul><ul><li>V=1/3lwh </li></ul><ul><li>V=1/3 pi r squared h </li></ul><ul><li>V=4/3 pi r cubed </li></ul>
    10. 10. NOW THE TRUTH <ul><li>HAS </li></ul><ul><li>TOTALLY </li></ul><ul><li>BEEN </li></ul><ul><li>REVEALED. IF YOU MISSED IT, THEN YOU ARE ONLY HUMAN! </li></ul>

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