Question

3 following are the properties of some special quadrilaterals. tick the correct shape which possesses such properties. properties rectangle rhombus square trapezoid all sides are congruent. both pairs of opposite sides are congruent. both pairs of opposite sides are parallel. all angles are congruent. exactly one pair of opposite sides are parallel.

Explanation:

• All sides are congruent: A rhombus has all sides equal in length, and a square (which is a special type of rhombus) also has all sides congruent. A rectangle has opposite sides congruent, and a trapezoid (in the non - isosceles and non - special cases) does not have all sides congruent.
• Both pairs of opposite sides are congruent: A rectangle, a rhombus, and a square (since it is a combination of rectangle and rhombus properties) have both pairs of opposite sides congruent. A trapezoid (in the non - isosceles and non - special cases) has only one pair of sides that may be parallel (and not necessarily congruent in the general case for both pairs).
• Both pairs of opposite sides are parallel: A rectangle, a rhombus, and a square (as they are parallelograms) have both pairs of opposite sides parallel. A trapezoid has exactly one pair of opposite sides parallel.
• All angles are congruent: A rectangle and a square have all angles equal (each angle is \(90^{\circ}\)). A rhombus has opposite angles congruent, and a trapezoid (in the non - isosceles and non - special cases) does not have all angles congruent.
• Exactly one pair of opposite sides are parallel: A trapezoid (by definition in the common definition where it is not a parallelogram) has exactly one pair of opposite sides parallel. A rectangle, rhombus, and square (as parallelograms) have two pairs of opposite sides parallel.

Answer:

• All sides are congruent: Rhombus, Square
• Both pairs of opposite sides are congruent: Rectangle, Rhombus, Square
• Both pairs of opposite sides are parallel: Rectangle, Rhombus, Square
• All angles are congruent: Rectangle, Square
• Exactly one pair of opposite sides are parallel: Trapezoid