    # TEST ON LINE

### Section:  Geometria Piana

1   Fundamental geometric entities

Contents: points, angles, segments, rays, lines

Number of questions: 20
Theshold: 75%
Maximum time: 20 minuti
2   Corners: classification and properties

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

Number of questions: 20
Theshold: 75%
Maximum time: 20 minuti
3   Polygons: general information

Definitions and first properties of polygons

Number of questions: 20
Theshold: 75%
Maximum time: 20 minuti
4   Criteria of congruence of any triangles

Sono richieste le seguenti conoscenze:

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

Number of questions: 20
Theshold: 75%
Maximum time: 20 minuti
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

Number of questions: 20
Theshold: 75%
Maximum time: 20 minuti
6   Perpendicular and parallel lines

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

Euclid's fifth postulate

Number of questions: 15
Theshold: 70%
Maximum time: 20 minuti
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

Number of questions: 20
Theshold: 75%
Maximum time: 20 minuti
8   Congruence criteria of triangles: summary

Congruence criteria for any triangles and right triangles

Number of questions: 20
Theshold: 75%
Maximum time: 20 minuti

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

Number of questions: 20
Theshold: 75%
Maximum time: 20 minuti
10   Bands of parallel lines and geometric loci

Parallel line sheaf theorem and consequences.

Main geometric loci.

Number of questions: 20
Theshold: 75%
Maximum time: 25 minuti
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

Number of questions: 20
Theshold: 75%
Maximum time: 20 minuti
12   Remarkable points of a triangle

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

Number of questions: 20
Theshold: 75%
Maximum time: 20 minuti
13   Remarkable points and Euler line

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

Number of questions: 20
Theshold: 80%
Maximum time: 20 minuti
14   Inscribed and Circumscribed Polygons

Definitions, properties , applications

Number of questions: 20
Theshold: 75%
Maximum time: 20 minuti
15   Equivalence of plane surfaces

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

Theorems of Pythagoras and Euclid
Number of questions: 20
Theshold: 75%
Maximum time: 20 minuti
16   The area of the polygons

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

Number of questions: 20
Theshold: 75%
Maximum time: 20 minuti
17   Pythagoras theorem and its applications

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

Number of questions: 20
Theshold: 75%
Maximum time: 25 minuti
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

Number of questions: 20
Theshold: 75%
Maximum time: 20 minuti
19   Similarity and Euclid's theorems

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

Number of questions: 20
Theshold: 75%
Maximum time: 25 minuti
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

Number of questions: 20
Theshold: 75%
Maximum time: 20 minuti
21   Geometric Transformations

Translation
Axial symmetry
Central symmetry
Rotation

Number of questions: 20
Theshold: 75%
Maximum time: 20 minuti