Final answer:
An isosceles trapezoid is characterized by having one pair of opposite sides parallel while the non-parallel sides are equal in length. The statement regarding diagonals being unequal is false as the diagonals of an isosceles trapezoid are equal in length.
Step-by-step explanation:
Regarding characteristics that apply to an isosceles trapezoid:
- (a) All sides are of equal length - This statement is false. In an isosceles trapezoid, only two sides (the non-parallel sides) are of equal length.
- (b) Two angles are right angles - This statement is typically false for an isosceles trapezoid, as by definition, it does not require right angles.
- (c) One pair of opposite sides are parallel - This statement is true. The definition of a trapezoid includes having at least one pair of parallel sides. In an isosceles trapezoid, the top and bottom sides are parallel.
- (d) The diagonals are of unequal length - This statement is false. In an isosceles trapezoid, the diagonals are of equal length.
The correct answer for an isosceles trapezoid is that one pair of opposite sides are parallel.