Download Monomior: is a constant variable or a porduct of a constant and one

Monomior: is a constant variable or a porduct of a constant and one or more variables, with the variables having
only not negative integer exponents
Polynomior: is a sum of finite number of monomiors
Divisibility: if a, b are positive integers than a is a divisior of b, if there is + integer such that a*q=b
Properties: a/a
if there a not =b and a/b ->not b/a
if a/b b/c -> a/c
Proof: a/b -> b=a*q
b/c -> c=b*q
Prime number: positive integers which has exactly 2 divisor
Compostive numbers: positive integers which have more than 2 divisiors
Common factorization: every number can be composed as a product of a prime number
G.C.D.: of two or more positive integers is the greatest positive integer that is a divisior of all the given integers
L.C.M.: of two or more integers is the lowest +integers which has each of the given integers as a factor
Relative prims: two or more +integers are called relative prims if GCD is one
Algebric fraction: is the quotient of two polynomiors.The denominator can't be a constract term.the domain of
the algebric fraction is the set of all real number, but the denominator isn't equal to zero.
The locus of points: is the sets of all points and only that point which is satisfy all the conditions.the Locus of
point are equidistant
Geometrical trasformations: our functions whoose domains and ranges are point sets.A point in the domain of a
geometrical transformation whoose image is the point itself its called fixed point.
Egybevágósági transf.: distance preserving
congurent
isometry
Distance preserving trans.: is a geometry trans. Ion which the langs of the image of any segment is equal to the
original segment
Reflection about a line: there is a given line t which will be the axis of of reflection. If P is on the line than its
image is point P itself. If Q isn't on the linethan from q we draw a perpendicular line to the axis t. Let the
interception point be t. We measure the distance of QP from t on the line on the opposite side of the axis, Q'
will be the image of Q
P=P'
Q
Properties: Straight line preserving
Segment preserving
Angle preserving
(fixed point, line)
Q'
Symmetrical Configuration: The planar configuration is said to be a symmetrical about a line if there is a
line(axis) in the plane of the configuration, such that, reflection about a line gives the image of a configuration
which is the configuration itself
Theorems:
The angles on the base of trapesium with non-parallel side are equivalent
The angles on the base of isoscales triangle are equivalent
The diagonals of the trapesium with non-parallel sides are equivalent
The symmetrical axis is a perpendicular bisector of the parallel sides of the trapesium with non-parallel sides
A
C A'
B
D B'
t
Reflection about a point: Let O be a given point it will be the centre of the reflection. If P not=O connect PO
measure that distance to the other side of O -> P'
P
O
P'
Symmetrical configuration: Configuration has a centre symmetry if there is a point such that reflection about a
point gives an image of the configuration which is the configuration itself.
Parallelogram is symmetrical about a point.
Opposite side of the parallelogram are equal
Midpoint of the diagonas is the centre of symetric
Opposite angles of the parallelogram are equal
Proof:
D
C=A'
o
A=C'
B
Reflect BC about O. (BC)'=AD, C'=A, BC ll AD (distance segment preserving)
Theorem: The middline of a paralelogram is equal and parallel to the other two sides.
D
C
p
q
A
B
p q is the midpoint of the trapesium.Connect the midpoints of the non-parallel sides (midline)
Theorem: The midline of a trapesium is parallel to the parallel sides and the lenghts is half as long as their siedes
Proof:
D
C=B'
p
q
A
B=C'
AD'A'D parallelogram
becouse segment preserving
reflect p about q >q'
Midline of a triangle:
A'
pp' is the midline of the new paralelogram
pp' ll DA' ll AB
pp'=AD'=AB
Q is the midpoint of pp'
C
reflect the triangle about r ABA'C paralelogram (distance
preserving)
p
(B') A
r
reflect p about r ->p' p is the midpoint of AC, p' is BA'
q
B (A')
A'
Theorem: The midline of the triangle is parallel to the side and the lenght is half as long as the lenght of a side.
Thalesz theorem: The two endpoint of a diameter of a circle and an arbitraly point on the circle can be connected
to form a right triangle the diameter is its hipotanuse.
Converse of the Thalesz theorem: The circum centre of the right triangle is the midpoint of the hipotanuse.
Proof:
B
C'
C
A
Construct a rright triangle, find its midpoint of AB=F
Reflect about F (AC'BC is a retangle (parallelogra with right angles))
CC' and AB are diagonas and half each other and equals
AF=BF=CF=C'F
Circumscribed quadrilateral is a convex quadrilateral whoose sides are tangent of a circle.
Theorem: In a circumscribed quadrilateral the sums of the lenght of the two pairs of opposite sides are equal.
A
e
B
f
C
h
D
e,f,g tangency point Ae=Ah=a
Be=Bf=b
stb.
A directed angle: alfa and point o are given in the plain the image of any point p is the point of p' such that the
angle p'op is equal to the given angle alfa and the distance of point o is itself and it is the centreof rotation
Vectors: is a directed line segement. The lenghts of a line segment is a magnitude of the vector and the direction
of a vector is measure by an angle. 2Vectors are equivalnt is they have the same direction magnitude.2 vectors
are opposite if they have the same magnitude but opposte direction. If the vectors has zero amgnitude and its
direction undefined O
Equation:is an equality between two expresson