Unit A: Geometry

Chapter 1: Polygons

Parallelograms, Rhombuses, and Kites

The properties of parallelograms, rhombuses, and kites are below.

Parallelograms
  • Opposite sides are equal in length.
  • Opposite interior angles are equal.
  • Diagonals are not equal in length.
  • Opposite diagonal angles are equal.
  • Both sets of opposite sides are parallel.
Rhombuses
  • All sides are equal in length.
  • Opposite interior angles are equal.
  • Diagonals are not equal in length.
  • All diagonal angles are 90°.
  • Both sets of opposite sides are parallel.
Kites
  • Two pairs of adjacent sides are equal.
  • The angles where the two pairs of adjacent sides meet are equal.
  • Diagonals x and y are generally not equal in length.
  • All diagonal angles are 90°.
  • Opposite sides are not parallel.

 
Calvin drew the following diagram of a square. Explain whether the square is part of the following quadrilateral categories. (Hint: For example, what characteristics of a rectangle does a square have?)

  1. Rectangle
  2. Trapezoid
  3. Parallelogram
  4. Rhombus
  5. Kite

 
 

a.
A square is a special case of a rectangle. A rectangle must have opposite sides that are equal and interior angles that are all 90°. These are both characteristics of a square.

b.
A square is not a trapezoid, because it has two pairs of parallel sides, not just one pair.

c.
A square is a special case of a parallelogram. A parallelogram must have opposite sides that are parallel to each other and equal in length. These are both characteristics of a square.

d.
A square is a special case of a rhombus. A rhombus must have all four sides that are equal in length and both sets of opposite sides that are parallel. These are both characteristics of a square.

e.
 A square is a special case of a kite (sometimes called a diamond). A kite must have two pairs of adjacent sides that are equal in length. This is also true of squares.