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.
Geometry is the study of figures. Plane geometry studies figures in a flat, two dimensional space called a plane. Solid geometry studies figures in a three-dimensional space. Coordinate Geometry Volume • Points, lines, and angles • Polygons-Triangles, Quadrilaterals…. • Perimeter and area • Circles
1. POINTS A POINT has no dimension and only position. 2.LINES AND THE ANGLESTHEY FORM 3. )INTERSECTING LINES AND RULES ABOUT ANGLES FORMED A LINE IS a continuous set of points having 1 dimension_length. A LINE SEGMENT IS a part of a line 3 WAYS TO DESCRIBE AN ANGLE ANGLE DEFINED: space formed when two lines meet at a point, ANGLE RELATIONSHIPS(adjacent/complementary) Intersecting lines (vertical/supplementary angles) Parallel lines
INTERSECTING/PARALLEL 3 WAYS TO DESCRIBE AN ANGLE ANGLE DEFINED ANGLE RELATIONSHIPS Intersecting lines
Angles equal/sides proportional vs. angles equal but sides same size and shape equal but sides same size and shape Similar vs. Congruent Polygons
Circles : a plane closed figure formed by a set of points equidistant from a fixed point called the center. Important terms What is pi? Ratio Circ: diameterr of a circle! So pi X diameter=circ The area of a circle: A= pi r squared Pi= 3.14 or 3.1 or 3 1/7 or 22/7 • Circumference: boundary • Radius: distance from center to any point on circumference. • Diameter-line segment passing through the center and ending on both ends at circ. • Chord: line segment having both endpoints on circ….longest one is diameter Secant: line passing throught the circle interesting it at 2 points Tangent: line intersecting the circle at only one point. Radius from that point is perpendicular to the tangent. Arc: a part of the circ. Semi-Cirlce- an arc that is ½ the circumference. Sector: The interior part of circle boredered by two radiii and the arc they intercept. Central Angle: verses inscribed angle…center point vs. point on circumference.
Coordinate Geometry Distance Sq.: (x2-x1)squared + (y1-y2)squared So the square root of the dist= square root of above Midpoint x1 + x2 /2, y1+y2/2= x midp..y midp. Slope: m = y2-y1/X2 - X1 • 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)
Volumes on Volumes Shape Formula V= e cubed V=pi r squared h V=1/3lwh V=1/3 pi r squared h V=4/3 pi r cubed • Cubes • Cylinders • Pyramids • Cones • Sphere
NOW THE TRUTH HAS BEEN REVEALED. IF YOU MISSED IT, THEN YOU ARE ONLY HUMAN! TOTALLY