Experiment set GEOMETRY 1

Inter-year

The geometry topics of this experiment set are inter-year topics: the first chapters are designed for introductory lessons in secondary school, while the following ones are for intermediate level. However, the order of the individual chapters does not need to be followed strictly for understanding.

The topics are:

• Angles: The introduction is done through an ungraduated angle model. Subsequently, students use a newly developed protractor, where misreading is prevented by the arrangement and position of the numerical values. With suitable triangles, the class can easily recognize the properties of adjacent, vertical, and complementary angles, as well as the angle sum in a triangle.

• Area: The equations for the areas of special quadrilaterals are developed by adding or rearranging partial areas. They can independently find the equations for the area of a triangle by applying already known methods. Similar triangles help in the use of the intercept theorems, as well as the trigonometric functions of the right triangle.
• Right triangle: Using an illustrative model, students discover the Thales theorem. They prove the Pythagorean theorem and the area theorems of Euclid with triangles, squares, and rectangles made of high-quality coloured acrylic glass. Certain connections can be assumed due to the use of the same colours.
• Intercept theorems and trigonometric functions: Similar triangles help in the use of the intercept theorems, as well as the trigonometric functions of the right-angled triangle.