Quadrilaterals that possess only one pair of equal length sides are specific types of four-sided polygons where exactly two of their sides share the same measurement, while the other two sides are of distinct lengths, differing from each other and from the equal pair. The most recognized named quadrilateral fitting this description is the isosceles trapezoid, though other general quadrilaterals can also be constructed to meet this precise condition.
Understanding "Only One Pair of Equal Length Sides"
To clarify, this property means that if a quadrilateral has four sides, let's call their lengths s1, s2, s3, s4:
- Exactly two of these sides are equal (e.g., s1 = s2).
- The remaining two sides are of different lengths (s3 ≠ s4).
- Crucially, the length of the equal pair must also be different from the lengths of the other two distinct sides (s1 ≠ s3 and s1 ≠ s4).
This configuration leads to side lengths that can be represented as (a, a, b, c), where 'a', 'b', and 'c' are all distinct positive values.
The Isosceles Trapezoid: A Key Example
The isosceles trapezoid (also known as an isosceles trapezium) is a classic example of a quadrilateral that consistently features only one pair of equal length sides.
- Definition: An isosceles trapezoid is a convex quadrilateral with at least one pair of parallel sides (called bases) and non-parallel sides (called legs) that are equal in length.
- Side Property: In an isosceles trapezoid, the two non-parallel legs are always equal in length. Assuming the two parallel bases are of different lengths and also different from the leg length, these legs constitute the only pair of equal length sides.
- Example: Consider an isosceles trapezoid with bases measuring 10 cm and 6 cm, and its two legs each measuring 5 cm. Here, the two 5 cm legs form the single pair of equal length sides (5 cm, 5 cm, 6 cm, 10 cm), perfectly matching the (a, a, b, c) structure.
General Quadrilaterals with Specific Equal Side Properties
Beyond the isosceles trapezoid, various general quadrilaterals can be specifically constructed to exhibit only one pair of equal length sides. These types are often described by their properties rather than having a unique common name.
Quadrilaterals with Exactly One Pair of Equal Opposite Sides
While a quadrilateral with only one pair of opposite sides parallel is commonly known as a trapezium (or trapezoid), a quadrilateral that possesses only one pair of opposite sides of equal length does not have a singular, widely recognized geometric name. Instead, it is typically described by its defining characteristic.
- Property: In such a quadrilateral, two opposite sides are equal in length, while the other two opposite sides are unequal, and all four side lengths are otherwise distinct.
- Example: Imagine a quadrilateral with sides measuring 5 cm, 3 cm, 5 cm, and 4 cm. Here, the two 5 cm sides are opposite and form the only pair of equal length sides.
Quadrilaterals with Exactly One Pair of Equal Adjacent Sides
Another configuration exists where the single pair of equal sides are adjacent to each other.
- Property: Two adjacent sides of the quadrilateral are equal in length, while the remaining two sides are unequal to each other and also unequal to the first pair.
- Example: A quadrilateral with sides measuring 5 cm, 5 cm, 3 cm, and 4 cm, where the two 5 cm sides are next to each other.
Distinguishing from Other Quadrilateral Types
It's important to differentiate these quadrilaterals from others that might seem similar but have more than one pair of equal sides:
- Kites: Kites have two distinct pairs of equal-length adjacent sides (e.g., sides of length (a, a, b, b) where a ≠ b). This means they have two pairs, not just one.
- Parallelograms (including Rectangles and Rhombuses): These quadrilaterals have two pairs of equal opposite sides (parallelograms and rectangles) or all four sides equal (rhombuses and squares). Therefore, they possess multiple pairs of equal-length sides.
Summary of Quadrilateral Types
| Quadrilateral Type | Side Length Properties | Example Side Lengths (distinct a,b,c) |
|---|---|---|
| Isosceles Trapezoid | Has one pair of equal non-parallel sides; other two sides (bases) are unequal and distinct from the equal pair. | (a, a, b, c) |
| General Quadrilateral (Equal Opp. Sides) | Has exactly one pair of equal opposite sides; other two sides are unequal and distinct from the equal pair. | (a, b, a, c) |
| General Quadrilateral (Equal Adj. Sides) | Has exactly one pair of equal adjacent sides; other two sides are unequal and distinct from the equal pair. | (a, a, b, c) |
Understanding these distinctions helps in accurately classifying quadrilaterals based on their specific side length characteristics. For more information on various quadrilateral properties, you can refer to resources like Wikipedia's Quadrilateral page.
