### 26.15.10 Checking whether an object in the plane is a parallelogram

See Section 27.11.14 for checking for parallelograms in 3D geometry.

The is_parallelogram command determines whether or not an object is a parallelogram.

- is_parallelogram takes G, a geometric object or a sequence of four points assumed to be the vertices of a quadrilateral.
- is_parallelogram(G) returns 1 if G is a parallelogram, but not a rhombus or a rectangle, returns 2 if G is a rhombus but not a rectangle, returns 3 if G is a rectangle but not a square, returns 4 is G is a square, and returns 0 otherwise.

#### Examples

is_parallelogram(i,-1+i,-1-i,1-i)

0 |  |  |  |  |  |  |  |  |  |

is_parallelogram(1+i,-1+i,-1-i,1-i)

1 |  |  |  |  |  |  |  |  |  |

Q:=quadrilateral(1+i,-1+i,-1-i,1-i); is_parallelogram(Q)

4 |  |  |  |  |  |  |  |  |  |

P:=parallelogram(-1-i,1-i,i,D); is_parallelogram(P[0])

1 |  |  |  |  |  |  |  |  |  |

Note that P[0] is a parallelogram since P is a list made of a parallelogram and vertex D.

affix(D)

−2+i |  |  |  |  |  |  |  |  |  |