Fundamental Mathematics/Geometry

Points distributed on a graph.
Line functions drawn on a graph.

Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer.

Points

Points are considered fundamental objects in Euclidean geometry.

Lines

By Euclid's axioms, a line can be drawn from 2 points. Example through 2 points A and B, we can draw the line AB.

A---------------B

Lines of interest

 Lines Definition Piture Perpendicular lines Two lines intecsect at a point to form an angle 90o ${\displaystyle {\overline {AB}}\perp {\overline {CD}}}$ Parallell lines Two lines do not intecsect each other ${\displaystyle {\overline {AB}}{//}{\overline {CD}}}$ Vector Line with its direction ${\displaystyle {\vec {AB}}}$

Angles

Two lines intersect at a point to form an angle between 2 lines . Example Line AB intersects line AC to form an angle A between 2 lines. Angle has a symbol ${\displaystyle \angle }$. Angles are measured in degrees (o) or radians (Rad). $\displaystyle \rad$

Example angle 90 degree is π radian

${\displaystyle \angle A=90^{o}={\frac {\pi }{2}}Rad}$

Geometric figures

Polygons

Polygons are shapes of <${\displaystyle n}$ sides and include:

 Polygon Definition Types Polygon Figure of n sides Triangle 3 sided polygon of Isosceles triangle | Right triangle | Equilateral Triangle Quadrilateral 4 sided polygon of Rectangle | Square | Parallelogram | Rhombus | Trapezoid