GEOMETRY

DIVIDE THE TRAPEZOID INTO TWO
How can you divide the trapezoid into two parts so that after being folded,
they will form a triangle?

CUTTING THE FIGURE INTO THREE
A plane figure consists of two squares such that AB = BC (see figure).
Divide the figure with two perpendicular cuttings so that after translation of
the three parts, they form one square.

THE CUTTING STRAIGHT LINE
A straight line cut a square in such a way that it divided the square’s
perimeter in a ratio of 9:7, and two sides of the square in a ratio 7:1 and 5:3.
In what ratio did the straight line divide the square’s area?

A MYSTERIOUS TRIANGLE
In a certain triangle, each angle is smaller than the sum of the two
remaining angles. What can we say about this triangle?

TRIANGULAR LAND
An island has the shape of a triangle. Which point lies farthest from the sea?

SLICED AND FLATTENED BOX
With a sharp knife, we cut the cardboard tetrahedron along three edges that
meet at the same vertex. Then, we flatten out the cardboard and put the
obtained plane figure on the table. Could the obtained figure be a square?