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 VolumesShape
• 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 TRUTHHAS TOTALLY
BEEN• REVEALED. IF YOU
MISSED IT, THEN YOU ARE ONLY HUMAN!
