Trisection Points of the Sides of a Rhombus

Proposed Problem 7

What is the figure formed by dividing the sides of a rhombus into three equal parts, and joining and extending adjacent points on either side of each vertex?

Conjecture

The figure formed by dividing the sides of a rhombus into three equal parts, and joining and extending adjacent points on either side of each vertex is a rectangle.

Hint

A rectangle is a quadrilateral with four right angles.

Please enable Java for an interactive construction (with Cinderella).

Drag free elements (free points A and B, semi free point C, or the side BC) to alter the rhombus ABCD and observe the measurment of angles of the figure EFGH, which is formed by joining and extending adjacent trisection points on either side of each vertex of the rhombus ABCD to check the correctness of the made conjecture.