# Apollinaria and math class

Updated: Sep 2

*Martina Vaculikova*

It was the first lesson of the first day of school, maths. The teacher, young and beautiful, with a strand of red hair on the back of her head, stood by the blackboard and greeted everyone who entered the classroom and helped them find a place at the desk.

The desks in the classroom stood in three rows. Two people could sit at each desk. Apollinaria decided to sit by the window. Behind the window was a beautiful sky and sea, and she liked to look out the window to think about something calmly.

"Hello, children!" said the teacher, "Today we start learning mathematics - the science of numbers and measurements. We will consider geometric shapes such as a triangle, a square, a rectangle. We will draw them in a notebook and count how many sides each figure has. " "There can be four triangles in every quadrilateral," thought Apollinaria, "No, actually more... there could be eleven, for sure... No, there could be twenty! I wonder if anyone in the class can find more triangles in a quadrilateral? Maybe I'll get a chance to ask!"

In the meantime, the teacher was drawing lines on the blackboard and talking about how parallel lines do not intersect, and that the line between two points is called a segment, which can be equal to the number of millimetres or centimetres. The segments can be put into a single line and get a longer segment. The lengths of several segments can be added together to get a sum - their total length. And if one segment is removed, then the sum of the lengths of all segments will be reduced by the length of this segment.

"Is it possible to calculate the sum of all sides of a quadrilateral?" thought Apollinaria, "and what will be the sum of the sides of the triangles inscribed in the quadrilateral? Will they coincide or differ?" These and other thoughts came to Apollinaria's mind as she listened to the teacher.