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rectangle (Definition)

Rectangle. A quadrilateral whose four angles are equal, that is, whose 4 angles are equal to $90^\circ$.

\includegraphics{rectangulo}

Any rectangle is a parallelogram.
This follows from angles $\angle BAD $ and $\angle ADC$ adding up $180^\circ$.

Since parallelograms have their opposite sides equal, so do rectangles. In the picture, $AB=CD$ and $BC=DA$.

Rectangles are the only parallelograms to be also cyclic (since opposite angles add up $180^\circ$.

Notice that every square is also a rectangle, but there are rectangles that are not squares

Rectangles have their two diagonals equal (since triangles $ABC$ and $ABD$ are congruent), A nice result following from this is that the quadrilateral obtained by joining the midpoints of the sides is a rhombus.

\includegraphics{rectangulo2}

Since $PQ$ joins midpoints of sides in triangle $ABC$, we have $PQ=CA/2$. Similarly we have $RS=CA/2$, $QR=BD/2$ and $SP=BD/2$ and thus the sides of quadrilateral $PQRS$ are all equal, in other words, $PQRS$ is a rhombus.




"rectangle" is owned by drini. [ owner history (1) ]
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See Also: quadrilateral, parallelogram, rhombus, parallelogram law, square

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Cross-references: joins, rhombus, sides, midpoints, congruent, triangles, diagonals, square, opposite, cyclic, opposite sides, parallelogram, angles, quadrilateral
There are 41 references to this entry.

This is version 2 of rectangle, born on 2001-12-12, modified 2004-03-08.
Object id is 1084, canonical name is Rectangle.
Accessed 19207 times total.

Classification:
AMS MSC51-00 (Geometry :: General reference works )

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