Is this a rectangle?

The definition of a rectangle is "a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square." Also a figure is "a shape which is defined by one or more lines in two dimensions (such as a circle or a triangle), or one or more surfaces in three dimensions (such as a sphere or a cuboid), either considered mathematically in geometry or used as a decorative design." ......sorry for the bad drawing...so neither definition says it has to connect....big fight with a friend so just trying to solve it lol.

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  • 4 weeks ago
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    A general purpose English dictionary does not have authority on mathematics.

    A rectangle connects. The thing in the drawing is not a rectangle but 4 lines that are almost a rectangle.

    Coloquially we approximate, because perfect rectangles don't exist in reality. Your drawing reminds of a rectangle, so you can call it a rectangle outside of a formal geometry setting. It is a cute rectangle.

    Also if it says "four right angles" how is that not connecting?

  • 4 weeks ago

    if there is not a continuous connection, then there is not a complete shape. In your case, you have two adjacent shapes, neither of which is a closed shape.  I think your definition of rectangle, or figure, or shape has to include "closed" as part of the definition.  A euclidian shape has to have a limit that segregates an interior region from an exterior region so that it is impossible to move from one region to the other without crossing that limit somewhere.

    There is a fault in your choice of definitions.

  • Anonymous
    4 weeks ago

    Unless the corners connect you don't have a plane figure, 

    you have a couple of pairs of intersecting lines. You need the Euclidean definition (he calls rectangles oblongs) and that is a figure that is right-angled but not equilateral.

  • 4 weeks ago

    Yes, it is.  You need to know that the given 4-sided figure, with both pairs of opposite sides equal in length, is a parallelogram.  You also need to know that a line perpendicular to one of two parallel lines is also perpendicular to the other.  That lets you conclude that the unlabeled angles are also right angles. 

    With 4 sides and 4 right angles, it's a rectangle!

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