Trisection Points of the Sides of a Rectangle

Proposed Problem 8

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

Hint

A rhombus is a quadrilateral with four equal sides.

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

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