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.

Points, lines, and angles

Polygons-Triangles, Quadrilaterals….

Perimeter and area

Circles

Solid geometry studies figures in a three-dimensional space.

Coordinate Geometry

Volume

1. POINTS

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 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

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.

INTERSECTING/PARALLEL

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 180Each angle is #/N (because number of sides=number of angles.)

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

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• 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.

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

Coordinate Geometry• 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)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

Volumes on Volumes

Shape

• Cubes• Cylinders• Pyramids• Cones• Sphere

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

NOW THE TRUTH

HAS

TOTALLY

BEEN• REVEALED. IF YOU

MISSED IT, THEN YOU ARE ONLY HUMAN!