Question

You're an amateur astronomer, and one night you seewhat appears to be a parallelogram in the constellationof Lyra. Explain how you could verify that the figure is aparallelogram.

Answer 1

Let:

`\begin{gathered} A=(x1,y1) \\ B=(x2,y2) \\ C=(x3,y3) \\ D=(x4,y4) \end{gathered}`

Points of the parallelogram

We can verify that it is a parallelogram if it satisfies the following conditions:

Two pairs of opposite sides are parallel.

Two pairs of opposite sides are equal in length.

Two pairs of opposite angles are equal in measure.

The diagonals bisect each other.

One pair of opposite sides is parallel and equal in length.

Adjacent angles are supplementary.

In order to make things a little quicker we can verify the following:

`\begin{gathered} |AC|=|BD| \\ |AB|=|CD| \end{gathered}`

And:

`\begin{gathered} AC\parallel BD \\ AB\parallel CD \end{gathered}`