Explanations about the scope of the contents covered in the course, as well as by the topics of each of its chapters.
Basic elements of plane geometry
Relations description
Definitions of line, half line, plane, half plane, circumference, circle, circle sector, circle segment
Definitions of: types of angles, bisector of an angle, bisector of a line segment and opening values of angles.
Postulates of plane geometry
Properties and definitions of line and plane
Collinearity definition
Line in a plane
Line by two points
Types of coplanar lines
Postulates of Euclides
Types of planes
Division of a line segment in sub segments of lines
Proportionality between lines segments
Definition of triangle
Perimeter of a triangle
Types of triangles
Similar triangles
Sum of internal angles of a triangle
Sum of external angles
Definitions of orthocenter, circumcenter and centroid of triangles
Area of triangles
Theorem of equivalences of area of triangles and parallelograms
Theorem of Pythagoras
Theorem of Carnot
Definition of quadrilateral, parallelogram, concave and convex
Perimeter of a quadrilateral
Sum of the internal and external angles
Definition of square and area of square
Circumference inscribed, circumscribed
Definition and areas of rectangles and parallelograms
Triangle and parallelogram
Golden segment and Golden rectangle
Definitions of circumference and circle
Definitions of radius and diameter
Perimeter of a circumference and circle
Area of circle
Circle sector and circular segment
Circular crown
Circular crown sector
Relative positions of two circumferences
Circumferences inscribed and circumscribed
Power of a point
Fibonacci and logarithmic spiral
Polygons concave and convex, regular and no regular
Important entities and structures
Formulas of relationships between elements of the side of the triangle
Sum of the external and internal angles of a polygon
Regular hexagon, triangle, dodecagon, square, octagon, decagon, pentagon, heptagon, nonagon, undecagon
Ellipse and eccentricity of ellipse
Construction of an ellipse
Inner and outer concentric circles
Length Latus Rectum of ellipse
Director circles of ellipse
Hyperbola and eccentricity of hyperbola
Construction of hyperbola
Auxiliary circle of hyperbola
Director circles of hyperbola
Parabola and construction of the parabola