Question

Use your knowledge of similar triangles to explain why the construction in the image divides the line segment into equal parts.

Answer 1

This image show how to divide a given line segment into a number of equal parts by using a compass and  ruler. First, draw the line AB. Secondly, draw a line above and divide into 5 equal distances to make a line AC. Third, using a compass by getting the distance of point C and B to be equal in the distance of point A and D, also getting the distance of point C to A to be equal to point B and D, then to make the Line DB. Finally divide into 5 equal parts by compass.

Answer 2

The construction creates a series of similar triangles where line segment AB represents one of the sides in each triangle. Because the top vertex of each similar triangle is drawn at a regular interval using a compass, the sides of each successive similar triangle increase in length at a constant rate. Therefore, each line segment created by the similar triangles will have the same length, breaking the given line segment into a series of equal parts.