TEST ON LINE

 1   Fundamental geometric entities

Contents: points, angles, segments, rays, lines

 2   Corners: classification and properties

Definition
Concave, convex, right, flat, round angle.
Complementary, supplementary, explementary angles.
Consecutive and adjacent angles

 3   Polygons: general information

Definitions and first properties of polygons

 4   Criteria of congruence of any triangles

Sono richieste le seguenti conoscenze:

- criteri di congruenza dei triangoli
- primo teorema dell'angolo esterno

 5   Inequalities in triangles and polygons

Projection of points and segments on a straight line.

Inequalities between sides and angles of a triangle

Inequalities between sides and angles of two triangles

 6   Perpendicular and parallel lines

Condition of parallelism and angles formed by straight lines cut by a transversal.

Euclid's fifth postulate

 7   Congruence criteria for right triangles

The following knowledge is required:

- congruence criteria for right triangles
- second exterior angle theorem
- sum of the interior and exterior angles of polygons

 8   Congruence criteria of triangles: summary

Congruence criteria for any triangles and right triangles

 9   Particular quadrilaterals

Parallelogram, rectangle, rhombus and square: definitions and properties.

 10   Bands of parallel lines and geometric loci

Parallel line sheaf theorem and consequences.

Main geometric loci.

 11   The circumference and the circle

The following knowledge is required:

- definition of circumference, circle and their parts
- chords and their properties
- relationship between two circles
- relationship between circle and straight line
- angles in the center and angles to the circumference

 12   Remarkable points of a triangle

Definition of: height, median, axis, bisector. 
Definition of: orthocenter, barycenter, circumcenter, incenter.

 13   Remarkable points and Euler line

Definition of: height, median, axis, bisector.
Definition of: orthocenter, barycenter, circumcenter, incenter.
Euler line.

 14   Inscribed and Circumscribed Polygons

Definitions, properties , applications

 15   Equivalence of plane surfaces

Equivalence between parallelograms, between triangles, between parallelograms and triangles, between triangle and trapezoid.

 16   The area of the polygons

Area of: triangles, quadrilaterals, regular polygons, inscribed and circumscribed polygons in a circle

 17   Pythagoras theorem and its applications

Pythagoras theorem: direct formula, inverse formulas and applications to the main polygons.

 18   Application of algebra to geometry

The following knowledge is required:
- Pythagoras theorem
- Euclid's theorems
- Particular right triangles
- Isosceles triangle and equilateral triangle
- Square and Hexagon

 19   Similarity and Euclid's theorems

Definition of similarity and applications to polygons and right triangles with Euclid's theorems

 20   The length of the circumference and the area of the circle

Knowledge of the following topics is required:

- circumference
- circle
- circular sector
- circular crown
- circular seed
- radiating arc

 21   Geometric Transformations

Translation
Axial symmetry
Central symmetry
Rotation