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

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

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meerkat18

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.

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.

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