Question

1. this straightedge and compass construction shows quadrilateral abcd. is abcd a rhombus? explain how you know. (from unit 1, lesson 7.)

Explanation:

Step1: Recall rhombus property

A rhombus has all - sides equal.

Step2: Analyze construction

In straight - edge and compass construction, when we construct a figure using circles centered at different vertices, if we consider the radii of the circles used in the construction. Let's assume that the construction involves circles centered at vertices of the quadrilateral. If the lengths of the sides of the quadrilateral \(AB\), \(BC\), \(CD\), and \(DA\) are all equal to the radii of the circles used in the construction (for example, if we construct the figure such that \(AB\) is a radius of a circle centered at \(A\) and \(B\), \(BC\) is a radius of a circle centered at \(B\) and \(C\), and so on), then \(AB = BC=CD = DA\).

Answer:

If the construction shows that \(AB = BC = CD = DA\) (by virtue of the radii of the circles used in the construction being equal to the side - lengths of the quadrilateral), then \(ABCD\) is a rhombus.