RectangleMathworldPlanetmath. A quadrilateralMathworldPlanetmath whose four angles are equal, that is, whose 4 angles are equal to 90.

Any rectangle is a parallelogramMathworldPlanetmath.
This follows from angles BAD and ADC adding up 180.

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.

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 midpointsMathworldPlanetmathPlanetmathPlanetmath of the sides is a rhombusMathworldPlanetmath.

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.

Title rectangle
Canonical name Rectangle
Date of creation 2013-03-22 12:02:29
Last modified on 2013-03-22 12:02:29
Owner drini (3)
Last modified by drini (3)
Numerical id 6
Author drini (3)
Entry type Definition
Classification msc 51-00
Related topic Quadrilateral
Related topic Parallelogram
Related topic Rhombus
Related topic ParallelogramLaw
Related topic Square