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The truth is not hiddenIn 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.
Points, lines, and angles
Perimeter and area
Solid geometry studies figures in a three-dimensional space.
1. POINTS 2.LINES AND THE ANGLESTHEY FORM3. )INTERSECTING LINES AND RULES ABOUT ANGLES FORMED
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 lineANGLE DEFINED: space formed when two lines meet at a point,Parallel linesANGLE RELATIONSHIPS(adjacent/complementary) Intersecting lines (vertical/supplementary angles)3 WAYS TO DESCRIBE AN ANGLE
ANGLE DEFINEDANGLE RELATIONSHIPS Intersecting lines3 WAYS TO DESCRIBE AN ANGLEINTERSECTING/PARALLEL
Angle relationships for intersecting linesAngle relationships for parallel lines
1) Angles opposite Each Other Are Equal and Called Vertical AnglesCorresponding Angles Defined2) Angles Adjacent to Each Other Are SupplementaryParallel lines definedPerpendicular Lines Intersect Ar Right AnglesAlternate Interior Angles formed by transverse lines.
Polygons: plane closed figure made up of straight line segments.
Remember type is defined by number of sides3/triangle, 4/quadrilateral, 5/pentagon, 6/hexegon
Similar verses Congruent:Angles equal/sides proportional vs. angles equal but sides same size and shapeSum of the Angles= (N-2) X 180Each angle is #/N (because number of sides=number of angles.)
Angles equal/sides proportional vs. angles equal but sides same size and shape equal but sides same size and shapeSimilar 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 Obtuselegs 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.
Circles : a plane closed figure formed by a set of points equidistant from a fixed point called the center.Important termsCircumference: 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 the circumference.
Sector: The interior part of circle boredered by two radiii and the arc they intercept.
Central Angle: verses inscribed anglecenter point vs. point on circumference.
What is pi? Ratio Circ: diameterr of a circle! So pi X diameter=circThe area of a circle:
A= pi r squared
Pi= 3.14 or 3.1 or
3 1/7 or 22/7
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)
Distance Sq.: (x2-x1)squared + (y1-y2)squaredSo the square root of the dist= square root of above
Midpointx1 + x2 /2, y1+y2/2= x midp..y midp.
Slope: m = y2-y1/X2 - X1
Volumes on VolumesShape
V= e cubedV=pi r squared hV=1/3lwhV=1/3 pi r squared hV=4/3 pi r cubed
NOW THE TRUTHHAS TOTALLYBEENREVEALED. IF YOU MISSED IT, THEN YOU ARE ONLY HUMAN!