# Definition: 1.22: Square, Rectangle, Rhombus, Rhomboid, Trapezium

And further of the trilateral figures: a right-angled triangle is that having a right angle, an obtuse-angled (triangle) that having an obtuse angle, and an acute-angled (triangle) that having three acute angles. And of the quadrilateral figures: a square is that which is right-angled, and equilateral, a rectangle that which is right-angled but not equilateral, a rhombus that which is equilateral but not right-angled, and a rhomboid that having opposite sides and angles equal to one another which is neither right-angled nor equilateral. And let quadrilateral figures besides these be called trapezia.

### Modern Definitions

A 4-sided figure quadrilateral) is called:

• a rectangle, if it has a right angles, but not all of its sides are congruent (i.e. have equal length),

• a rhombus, if it all it sides are congruent but it has no right angles,

• a parallelogram (or rhomboid), if it its opposite sides are congruent to one another, but it has no right angles,

• a trapezium, if it has one pair of opposite sides parallel to each other.

Thank you to the contributors under CC BY-SA 4.0!

Github:

non-Github:
@Calahan
@Casey
@Fitzpatrick

### References

#### Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014