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| Special Parallelograms |
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| Rectangles, rhombuses and squares belong to the set of parallelograms. Each of these may be defined as a parallelogram as follows: |
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 A rectangle is an equiangular parallelogram. |
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 A rhombus is an equilateral parallelogram. |
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 A square is an equilateral and equiangular parallelogram. |
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| Thus a square is both a rectangle and a rhombus. |
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| The relations among the special parallelograms can be pictorially represented in the figure given below: |
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| Since every rectangle and every rhombus must be a parallelogram, they are shown as subsets of a parallelogram and since a square is both a rectangle and rhombus, it is represented by the overlapping shaded section. Let us now define each of these special types of parallelograms. |
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| A rectangle is a parallelogram with one of its angle a right angle. |
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| It can be shown that each angle of a rectangle is a right angle. |
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| (sum of interior angles on the same side of transversal AB) |
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| Corollary: Each of the four angles of a rectangle is a right angle. |
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| A rhombus is a parallelogram with a pair of its consecutive sides equal. |
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| ABCD is a rhombus in which AB=BC. |
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| Since a rhombus is a parallelogram, AB=DC and BC=AD. |
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| Thus AB=BC=CD=AD. |
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| Corollary: All the four sides of a rhombus are equal (congruent). |
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| A square is a rectangle with a pair of its consecutive sides equal. |
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| Since square is a rectangle, each angle of a rectangle is a right angle and AB=DC, BC=CD. |
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| Thus AB=BC=CD=AD. |
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| Each of the four angles of a square is a right angle and each of the four sides is of the same length. |
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