Mathematics Pages

Mathematics is the truth someone could demonstrate S.G.

Scope: This web site underlines some basics mathematics theory from the following topics: arithmetic, algebra, geometry, trigonometry (in construction), calculus (in construction), all needed for studying more advanced topics.

In the future the topics will be listed for various grades.(for now the web site is under construction, and its display may not be pleased to the eye, but the focus was on the math knowledge and solving techniques than on the web design)

NOTE: For now you need to scroll down to see the exercises. In the future you will need to click the topic and it will pop up. The Back to Top does not work yet.

Arithmetics and Algebra

Geometry

Geometry 2D

Geometry 3D

Trigonometry(to come)

Calculus(to come)

Arithmetics and Algebra

Basic things you need to know in Mathematics-Arithmetics

Set of Numbers: N, W, I, Q, nonQ, R, C; Examples
Adding, subtracting, multiplying, dividing positive and negative numbers Examples
Simplify the math expressions with brackets Examples
Fractions and decimal numbers Examples
Factor numbers, find the common factors between numbers and math expressionsExamples
Powers, and calculations of mathematical expressions using exponentsExamples
Radicals, and calculations using radicalsExamples
Percentage, calculations and word problems using percentagesExamples

Basic things you need to know in Mathematics-Algebra

Simplify expressions with variables. Addition, subtraction, multiplication, divisionExamples
Solve equations with 1 variableExamples

Medium Mathematics Knowledge - Algebra

Solve and graph linear equationsExamples
Solve and graph systems of 2 linear equationsExamples
Solve equations with 3 variables
Solve inequalities
Solve Quadratics. Graph quadraticsExamples
Polynomial Functions. Graphs. Word problems
LogarithmsExamples

Geometry

Geometry 2D

Geometry 3D

Geometry 2D Tips

Test your knowledge in Geometry 2D

LINEs and ANGLES

A line is made by infinity of points
Each side of a line could be considered a 180 degrees angle
Three points are on a line if they can form an 180 degrees angle
Parallel lines intersected by a secant form pair of equal angles (internal, alternate, corespondent)
If two lines intersected by a secant form at least a pair of equal angles (internal, alternate, corespondent types), the two lines are parallel
Two perpendicular lines on the 3rd one are parallel
If one of the two parallel lines is perpendicular on a 3rd line, than the other parallel is perpendicular on the 3rd one
The shortest distance from a point to a line is the perpendicular from that point to the line
The angles with parallel lines are equal or supplementary (their sum is 180 degrees)
The angles with perpendicular sides are equal
The bigger the angle in a triangle, the larger the opposite side
Three parallel lines intersected by 2 secants form equal segment ratios (Thales Theorem)
The angle with the vertex in the center of the circle and the sides chords in the circle has the same measurement with the circle arc between its sides.
The distance from a point to a line is the measurement of the perpendicular from that point to the line
The bisector of an angle is the line which divides the angle in two equal angles
The perpendicula bisector is a line perpendicular on the middle of a segment
All the points on a perpendicular bisector are equaly distanced to the segment ends

TRIANGLES

The types of triangles: scalene, isosceles, right triangle, equilateral
The sum of interior angles of a triangle is 180 degrees
In a triangle, the sum of two sides is bigger than the third side
In a triangle, the difference of two sides is smaller than the third side
The exterior angle of a triangle is formed by the elongation of one side and another side of the triangle
The measurement of the exterior angle of a triangle is equal with the sum of the measurements of the interior angles of the triange non-adjacent to it
The important lines in a triangle are: the height or altitude, the bisector, the median and the perpendicular bisector
The height is the line started from a triangle vertex and ends perpendicular on the oposite site
The area of a triangle is the (height x base)/2, and it is the same for all the heights and bases used
All the three heights of a triangle intersect in a single point, H, named orthocenter. Note: if the triangle has an obtuse angle the heights intersect outside the triangle
The bisector in a triangle intersects the oposite side, and makes a ratio of the segments created equal with the ratio of the sides starting from its vertex
The three bisectors in a triangle intersect in a single point, the center of the inscribed circle in the triangle in the triangle
The three medians in a triangle intersect in a single point, G, called the center of mass. It is located at 2/3 from the vertex and 1/3 from the base of the triangle
All the heights of a right triangle intersect in the 90 degree vertex
Any triangle can be circumscribed to a circle
The center of the circle circumscribed to a triangle is found at the intersection of the triangle perpendicular bisectors
Any triangle can be inscribed in a circle
The center of the circle inscribed in a triangle, is found at the intersection of triangle bisectors
The middle line in a triangle joins the middles of two sides in a triangle. It is parallel to the third side and half of its length
In a triangle, the sum of two sides is bigger than the third side
In a triangle, the sum of two sides is bigger than the third side

Geometry 3D - basic theorems

3 non-colinear points determine an unique plane
A line not contained in the plane is parallel with the plane if it is parallel with any line in the plane
A line is contained in a plane if it has 2 point contained in the plane
A line is perpendicular on a plane if it is perpendicular on any line in the plane
A line is perpendicular on the plane if it is perpendicular on 2 intersecting lines contained in the plane
The angle between a line and a plane is the one formed by the line and its projection on the plane
The angle between 2 planes is the angle between 2 lines, each contained by one of the plane, and perpendicular on their intersection line
If the intersection line of 2 planes is perpendicular on the 3rd one, than the 2 planes are perpendicular on the 3rd one
The theorem of the 3 perpendiculars. Draw a line d1 perpendicular on a plane P, with the intersection M. Draw a random line d2 in the plane P, not intersecting line d1. Draw a perpendicular line from point M on line d2, and mark the intersection with N. Than any line draw from any point on line d1 joining point N is perpendicular on line d2. The reciprocals are true.