Rhombus - Basic Properties

Basic Properties

Every rhombus has two diagonals connecting pairs of opposite vertices, and two pairs of parallel sides. Using congruent triangles, one can prove that the rhombus is symmetric across each of these diagonals. It follows that any rhombus has the following properties:

  1. Opposite angles of a rhombus have equal measure.
  2. The two diagonals of a rhombus are perpendicular; that is, a rhombus is an orthodiagonal quadrilateral.
  3. Its diagonals bisect opposite angles.

The first property implies that every rhombus is a parallelogram. A rhombus therefore has all of the properties of a parallelogram: for example, opposite sides are parallel; adjacent angles are supplementary; the two diagonals bisect one another; any line through the midpoint bisects the area; and the sum of the squares of the sides equals the sum of the squares of the diagonals (the parallelogram law). Thus denoting the common side as a and the diagonals as p and q, in every rhombus

Not every parallelogram is a rhombus, though any parallelogram with perpendicular diagonals (the second property) is a rhombus. In general, any quadrilateral with perpendicular diagonals, one of which is a line of symmetry, is a kite. Every rhombus is a kite, and any quadrilateral that is both a kite and parallelogram is a rhombus.

A rhombus is a tangential quadrilateral. That is, it has an inscribed circle that is tangent to all four of its sides.

Read more about this topic:  Rhombus

Famous quotes containing the words basic and/or properties:

    “Our basic ideas about how to parent are encrusted with deeply felt emotions and many myths. One of the myths of parenting is that it is always fun and games, joy and delight. Everyone who has been a parent will testify that it is also anxiety, strife, frustration, and even hostility. Thus most major parenting- education formats deal with parental emotions and attitudes and, to a greater or lesser extent, advocate that the emotional component is more important than the knowledge.”
    —Bettye M. Caldwell (20th century)

    “A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
    —Ralph Waldo Emerson (1803–1882)