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The truth is not hidden l.jpg

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 l.jpg

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


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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


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INTERSECTING/PARALLEL

3 WAYS TO DESCRIBE AN ANGLE

ANGLE DEFINED

ANGLE RELATIONSHIPS

Intersecting lines


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Polygons: plane closed figure made up of straight line segments.


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Angles equal/sides proportional vs. angles equal but sides same size and shape equal but sides same size and shape

Similar vs. Congruent Polygons


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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.


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Coordinate Geometry

Distance Sq.: (x2-x1)squared + (y1-y2)squared

So 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

  • 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)


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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


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NOW THE TRUTH

HAS

BEEN

REVEALED. IF YOU MISSED IT, THEN YOU ARE ONLY HUMAN!

TOTALLY


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