Draw 8 triangles from 5 lines

What you need:

• a sheet of squared paper or graph paper
• Crayon
• ruler

Geometric basics of triangles

• Each triangle, as the name suggests, has three corners and also three sides that connect these corners. The triangles are differentiated according to the size of the angles that the corners occupy and the length of the sides.
• There are isosceles, equiangular, equilateral and right triangles.
• With right triangles, an angle is a right angle, so it measures exactly 90 °. The two sides that lie against this angle are called cathets. The third side is the hypotenuse.
• You can now connect the midpoint of one side of the triangle to the opposite corner. This line is called the bisector. Since a triangle has three sides, it also has three bisectors, one for each side. These three bisectors intersect at one point, the center of gravity of the triangle.
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How to draw 8 triangles with 5 strokes

•  8 triangles have 24 sides according to a simple calculation. So you theoretically need 24 lines to draw 8 individual triangles. You can also place the triangles next to each other or nest them in order to achieve the goal with fewer lines.


Halve the triangle - this is how it's done

Halving any triangle is definitely a trick behind it. In …

• To solve the problem of drawing 8 triangles from 5 strokes, start with a right triangle. The right angle is at the bottom right. One cathetus lies horizontally and the other runs vertically upwards.
• You have now drawn a triangle with three lines. That was easy. But there are still 7 more triangles missing and you can only draw 2 lines!
• The solution is very simple. Draw in the bisector of the hypotenuse and the bisector of one of the two cathets! That was all, you made it. Go ahead and count, 5 lines and 8 (of course) overlapping triangles!