How to Divide a Triangle Into Three Triangles

There are a number of ways in which triangles can be divided in order to create three triangles within the original shape. If the simple rules below are followed, an infinite number of triangles can be created, all differing in size and shape. This is the beauty of triangles for mathematicians. Although such a simple and basic shape, its form creates questions that the world's best mathematicians cannot even grasp.

Instructions

Triangle 1

1. Draw a triangle on a piece of paper. Ensure the base of the triangle is horizontal and sits nearest the base of the sheet.

2. Draw a dot anywhere within the triangle just drawn.

3. Draw a straight line to the dot from each of the corners of the triangle. All lines should connect, creating three triangles within the triangle.

Triangle 2

1. Draw a triangle on a piece of paper. Ensure the base of the triangle is horizontal and sits nearest the base of the sheet.

2. Draw a straight line from the top of the triangle to the base of the triangle.

3. Draw another straight line from the top of the triangle to the base of the triangle. This will form three triangles within the triangle.

Triangle 3

1. Draw a triangle on a piece of paper. Ensure the base of the triangle is horizontal and sits nearest the base of the sheet.

2. Draw a straight line from the top of the triangle to the base of the triangle.

3. Draw another straight line at the location where the line drawn in the previous step meets the base of the triangle up to any point on the upper two sides of the triangle. This will form three triangles within the triangle.

Triangle 4

1. Draw a triangle on a piece of paper. Ensure the base of the triangle is horizontal and sits nearest the base of the sheet.

2. Draw a straight line from the top of the triangle to the base of the triangle.

3. Draw a straight line from one of the bottom edges of the triangle to any point along the straight line drawn in in the previous step. This will form three triangles within the triangle.

References

• Math Puzzle: Triangles