Definition: A rectangle is quadrilateral with 4 right angles (90°).

Rule: Opposite sides of a rectangle are congruent (of equal length).

Proof: By the definition of a rectangle, it follows that every rectangle is a parallelogram. We showed that opposite sides of a parallelogram are congruent. It follows that opposite sides of a rectangle are congruent.

Interactivity 1: Rectangles   Directions for interactivity

Click and drag the slider buttons to change the size. Click and drag point B to move and point А to rotate.

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Basic formulas for rectangles with sides a and b: the perimeter is: L=2(a+b) , and the area is: A=ab .

Examples for perimeter and area of rectangles

Check the following examples using the above interactivity.

a b Perimeter: L=2(a+b) Area: A=ab
3 \,cm 4 \,cm 2(3 \,cm+4 \,cm)= 14\,cm 3 \, cm \cdot 4 \,cm=12 \,cm^2
2,5 \, m 4 \,m 2(2,5 \,m+4 \,m) =13 \,m 2,5 \,m \cdot 4 \,m=10 \,m^2
0,07 \,m 60 \,mm 2(7 \,cm+6 \,cm) =26 \,cm 7 \,cm \cdot 6 \,cm=42 \,cm^2
0,07 \,m 60 \,mm 2(0,07 \,m+0,06 \,m) =2,6 \times 10^{-1} \,m 0,07 \,m \cdot 0,06 \,m=4,2 \times 10^{-3} \,m^2

Interactivity 2: Construct a rectangle

1. Examine the rectangle in the above interactivity..

2. Now construct a rectangle with the same properties. If you need help with the steps , click here to open a new window with  directions?.

Check whether your construction is stable - Is your construction always a rectangle no matter what slider or point you move?
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Equivalent definition:
  • A rectangle is a parallelogram with one interior right angle (from this, it follows that all interior angles are right angles).

Theorems

  • A rectangle is completely determined by the lengths of two adjacent (neighboring) sides.
  • The diagonals of a rectangle bisect each other (cut each other in half). (This follows from the fact that a rectangle is a parallelogram.)

The diagonals of a rectangle are congruent (the same length) Interactivity

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  1. By definition of rectangle, opposite sides are the same length, so: | \overline{BC} |=| \overline{AD} | .
  2. Analogously, <BCD = 90^\circ = <CDA .
  3. Using the condition Side-Angle-Side, the triangles \Delta BCD and \Delta CDA are congruent (equivalent).
  4. It follows that the diagonals \overline{DB} и \overline{CA} are congruent, that is, they are the same length.

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Page last modified on April 05, 2008, at 03:01 PM