Question

this straightedge and compass construction shows quadrilateral abcd. is abcd a rhombus? yes. no. explain how you know.

Explanation:

Step1: Recall rhombus property

A rhombus has all - sides equal.

Step2: Analyze side - lengths from construction

In the straight - edge and compass construction, since the circles are drawn with the same radius (implied by the construction method), we have \(AB = BC=CD = DA\). The lengths of the sides of the quadrilateral \(ABCD\) are equal because the segments are radii of congruent circles.

Answer:

Yes. In the straight - edge and compass construction, the lengths of \(AB\), \(BC\), \(CD\), and \(DA\) are equal as they are radii of congruent circles, and a quadrilateral with all sides equal is a rhombus.