TEST ON LINE
Section: Geometria Piana
Contents: points, angles, segments, rays, lines
Definition
Concave, convex, right, flat, round angle.
Complementary, supplementary, explementary angles.
Consecutive and adjacent angles
Definitions and first properties of polygons
Sono richieste le seguenti conoscenze:
- criteri di congruenza dei triangoli
- primo teorema dell'angolo esterno
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
Condition of parallelism and angles formed by straight lines cut by a transversal.
Euclid's fifth postulate
The following knowledge is required:
- congruence criteria for right triangles
- second exterior angle theorem
- sum of the interior and exterior angles of polygons
Congruence criteria for any triangles and right triangles
Parallelogram, rectangle, rhombus and square: definitions and properties.
Parallel line sheaf theorem and consequences.
Main geometric loci.
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
Definition of: height, median, axis, bisector.
Definition of: orthocenter, barycenter, circumcenter, incenter.
Definition of: height, median, axis, bisector.
Definition of: orthocenter, barycenter, circumcenter, incenter.
Euler line.
Definitions, properties , applications
Equivalence between parallelograms, between triangles, between parallelograms and triangles, between triangle and trapezoid.
Area of: triangles, quadrilaterals, regular polygons, inscribed and circumscribed polygons in a circle
Pythagoras theorem: direct formula, inverse formulas and applications to the main polygons.
The following knowledge is required:
- Pythagoras theorem
- Euclid's theorems
- Particular right triangles
- Isosceles triangle and equilateral triangle
- Square and Hexagon
Definition of similarity and applications to polygons and right triangles with Euclid's theorems
Knowledge of the following topics is required:
- circumference
- circle
- circular sector
- circular crown
- circular seed
- radiating arc
Translation
Axial symmetry
Central symmetry
Rotation