What is a quadrilateral that has exactly 2 congruent consecutive sides? Would it be either a parallelogram and/or a trapezoid?
1 Answer
As a rule almost all kites (but not when the kite is also either a rhombus or a square). As exception some trapezoids (not isosceles ones) and some trapeziums.
Explanation:
To remind definitions of the kinds of quadrilaterals refer to
https://www.mathsisfun.com/quadrilaterals.html
A parallelogram can never satisfy the condition because it has two congruent non-consecutive sides (in fact the two other sides are also congruent to each other).
Using the reductio ad absurdum argument, if any of a pair of its non-consecutive sides is congruent to a third one then the parallelogram would have more than two sides congruent to themselves, what doesn't satisfy the condition of the problem.
Since a square, a rhombus and a rectangle are also parallelograms, they are also excluded.
In a kite, by definition a pair of its adjacent (or consecutive) sides are congruent to each other as well as the other pair of adjacent sides. So the condition is satisfied.
In a trapezoid (US English) if one of the bases is congruent to one and only one (that excludes the isosceles trapezoids) of the adjacent sides the condition is satisfied. This is possible but since it doesn't result from the definition of the trapezoid, only some trapezoids satisfy the condition, and they are a special kind of trapezoid.
The same is valid for a trapezium (US English), where there are only the basic restrictions (sum of lengths of sides, sum of angles) of a generic quadrilateral, it is possible to make two consecutive sides congruent to each other and make the two other sides different of each other and of the first two sides. So, for such a special kind of trapezium, the condition is satisfied.
