# BASIC GEOMETRY – ENGLISH – CHAPTERS

Introduction

Explanations about the scope of the contents covered in the course, as well as by the topics of each of its chapters.

Chapter 1

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.

Chapter 2

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

Chapter 3

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

Chapter 4

Definition of quadrilateral, parallelogram, concave and convex

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

Chapter 5

Definitions of circumference and circle

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

Chapter 6

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

Chapter 7

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