Question

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

Explanation:

• All sides are congruent: A rhombus has all sides equal in length. A square also has all sides congruent (since a square is a special type of rhombus).
• Both pair of opposite sides are congruent and parallel: A rectangle has both pairs of opposite sides congruent and parallel. A rhombus (with its all - side - congruent property) also has both pairs of opposite sides parallel (by the definition of a parallelogram, and a rhombus is a parallelogram). A square, being a combination of a rectangle and a rhombus, has this property too.
• All angles are congruent: In a rectangle, all angles are right angles (\(90^{\circ}\)), so they are congruent. In a square, all angles are also right angles.
• Exactly one pair of sides are parallel: By definition, a trapezoid has exactly one pair of parallel sides.

Answer:

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