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A point
represented as a small dot has no length, with or thickness.
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a line
connecting two points along the shortest possible path, has no thickness and extends infinitely in both directions.
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A plane
is a flat surface with no thickness and no boundaries. does not extend indefinitely and it does have a thickness.
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A ray
is a half-line with its endpoint included.
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Half-lines
any point on the line divides the line into three parts-the point and two half-lines.
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angle
is formed by the union of two rays that have a common endpoint.
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A ray is
called the initial side and the other the terminal side.
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vertex
the common endpoint of and angles initial side and terminal side is the vertex of the angle.
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angels are measures how?
by degrees.
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an acute angle
measures less than 90 degree.
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a right angle
on quarter of a complete rotation, measures 90 degrees.
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an obtuse angle
measures more than 90 degrees but less than 180 degrees.
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straight angle
on half a complete rotation, measures 180 degrees
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protractor
used for finding the degree measure of and angle.
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complementary angles
two angles whose measures have a some of 90 degrees
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supplementary angles
two angles whose measures have a sum of 180 degrees
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vertical angles
when two lines intersect the opposite angles
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parallel lines
are lines that lie in the same plane and have to points in common.
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intersecting lines
two different lines in the same plane are not parallel, they have single point in common.
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perpendicular lines
lines intersect at an angle of 90 degrees
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Transveral
pair of parallel lines with a third line that create 8 angles.
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alternate interior angles
interior angles that do not have a common vertex on alternate sides of the transversal
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alternate exterior angles
exterior angles that do not have a common vertex on alternate sides of the transversal
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corresponding angles
one interior and one exterior angle on the same side of the transversal
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theorem
a conclusion that is proved to be true through deductive reasoning
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triangle
is a geometric figure that has three sides, all of which lie on a flat surface or plane.
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closed geometric
beginning point and ending point are the same the triangle is closed.
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acute triangle
all angles are acute
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right triangle
one angle measures 90 degrees.
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obtuse triangle
one angle is obtuse
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isosceles triangle
two sides have equal length.
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equilateral triangle
all sides have equal length. 60,60,60 degrees
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scalene triangle
no two sides are equal in length.
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scale drawings
figures that have the same shape, but not the same size.
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hypotenuse
the side opposite the 90 degree angle.
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Pythagorean theorem
the lengths of the three sides of a tight triangle.
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Tessellation or tiling
is a pattern consisting of the repeated use of the same geometric figure to completely cover a plane, leaving no gaps and no overlaps.
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Circle
is a set of points in the plane equally distant form a given point, its center.
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radius is
a line segment from the center to any point on the circle.
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diameter
is a line segment through the center whose endpoints both lie on the circle.
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circumference
distance around a circle
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Volume
amount of space occupied by a solid object, determined by the number of cubic units it takes to fill the interior of that object.
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rectangular solid
the volume of the box.
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Cube
if the length, width, and height are the same, the rectangular solid.
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polyhedron
a solid figure bounded by polygons. a rectangular solid is and example.
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rectangular solid
is bounded by sex rectangles, called faces.
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Pyramid
is a polyhedron whose base is a polygon and whose side are triangles.
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Right circular cone inside a cylinder.
sharing the same circular base as the cylinder.
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Sphere
is the set of points in space equally distant from a given point of its center.
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surface area
are of the outer surface of a three dimensional object.
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Three fundamental trigonometric ratios?
since, cosine, tangent.
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Angle of elevation
an angle formed by a horizontal line and the line of sight to an object that is above the horizontal line.
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Angle of depression
angle formed by a horizontal line and the line of sight to an object that is below the horizontal line.
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A vertex is a point is?
an edge is a line segment or curve that starts and ends at a vertex.
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vertices and edges form a graph by?
the vertex with an odd number of attached edges is and odd vertex. a vertex with an even number of attached edges is a even vertex.
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Traversable?
it can be traced without lifting the pencil from the paper and without tracing an edge more than once.
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Topology
shapes that can be twisted, stretched, bent, and shrunk.
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Genus
Gives the largest number of complete cuts that can be made in the object without cutting the object into two pieces.
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Topolgically equivalent
objects with the same genus.
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Iteration
a rule again and again to create a self-similar fractal like the broken-up triangle.
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fractal geometry
broken up or fragmented shapes.
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euclidean geometry euclid
given a point not on a line, there is one and only one line through the point parallel to the given line.
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hyperbolic geometry lobachevsky, bolyai
given an point not on a line, there are an infinite number lines through the point that do no intersect the given line.
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Elliptic geometry Riemann
there are no parallel lines.
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Klein bottle
Klein bottle passes through itself without the existence of a hole, which is impossible in three-dimensional space.
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 is what formula?
rectangle
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 is what formula?
square
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 is what formula?
parallelogram
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 is what formula?
triangle
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 is what formula?
Trapezoid
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 is what formula?
standard form for circle.
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 is what formula?
hyperbola
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is what formula?
Quadratic functions
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is what formula?
Prism
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 is what shift in a conics
UP and Down.
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 what shift is this in conic
left and right.
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C is what in conics
the x intercept.
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 is what formula?
for a parabola
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corresponding line
1,5,-3,7-2,6-8,4
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Pythagorean theorem. C is the longest side of a triangle.
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 is what form?
general conic equation
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Products to create conic equation is
2 variables and at least one has is squared.
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 is what?
Ellispe
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 is what?
hyperbola
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