Constructing an equilateral quadrilateral I

Constructing an equilateral quadrilateral I


To demonstrate a construction of a rhombus, and to differentiate between a special construction and a general one.

Two video demonstrations of compass and straight-edge constructions show how to construct a general rhombus.

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This packet assumes that you know how to construct an equilateral triangle. If you do not, you should check out my packet on this topic.

In this packet you will learn to construct an equilateral quadrilateral (a rhombus). The first construction will work, but it will be a special figure-one that has properties that are not true of all equilateral quadrilaterals. The second construction will be a general quadrilateral.

Don't forget that you want to be thinking about why these constructions work, not just memorizing the steps. If you're only memorizing steps, you're not learning any geometry.

First try-a special equilateral quadrilateral

This video demonstrates constructing an equilateral quadrilateral with special properties.

Second try-a general construction

This video demonstrates a general construction-one that results in an equilateral quadrilateral with no extra properties. Any geometric relationships we see in this construction should be true of all equilateral quadrilaterals. This was not necessarily true of the special construction in the first video.


So this second construction works-it constructs an equilateral quadrilateral-a rhombus. And it constructs a general rhombus-one with no other special properties.

Notice that the segment we started with (EF in the second video) forms a side of the rhombus. So we will call this construction, Rhombus construction 1 (side).

But the starting segment need not be the side of our rhombus. Instead, it can be a diagonal. That construction will be Rhombus construction 2 (diagonal) and it will be the focus of another packet.