THE QUADRILATERAL

1
THE QUADRILATERAL
A quadrilateral is plane figure with four sides
and four angles

• Its named of the quadrilateral by taking the
  vertices in order either in clockwise or
  anticlockwise direction.
• The line segments AC and BD that joint the
  opposite vertices are called diagonals.
• The sum of the four angles of quadrilaterals
  equals 3600.

2
1. PARALLELOGRAM
A parallelogram is a quadrilateral with two pairs
of opposite sides parallel.

• Properties of the parallelogram
• 1. AB // DC and AD // BC.
• 2. The opposite sides of parallelogram are equal
  in length, i.e., AB DC and AD BC.
• 3. The diagonals of a parallelogram bisect each
  other,i.e., OA OC and OB OD.
• 4. The opposite angles of a parallelogram are
  equal, i.e., ltA ltC and ltB ltD.
• 5. Two consecutive angles of a parallelogram are
  supplementary angles

3
2. RECTANGLE
a rectangle is a parallelogram where all its
angles are right angle.

• The properties of the parallelogram are also of a
  applicable to a rectangle.The diagonal of a
  rectangle a equal in length, i.e., ACBD.

4
3. SQUAREA square is a rectangle which all sides
are equal in lengths.

• Properties of the square ABCD
• ABBCCDDA
• All its angles are right angles, ltAltBltCltD 900
• The diagonals of a square are equal in length,
  i.e. ACBD
• The diagonals of a square bisect each other at
  right angles.

5
4. RHOMBUSA rhombus is a parallelogram which all
sides are equal in lengths.

• Properties of the rhombus
• ABBCCDDA
• The diagonals of the rhombus bisect each other at
  right angles, ltAOBltBOCltCOD
• ltDOA900 and OAOC, OBOD
• The diagonals of rhombus bisect the angles,i.e.
  ltDAOltBAO

6
5. KITEA kite is a quadrilateral with 2 pairs of
equal adjacent sides.

• Properties of the kite
• ABBC and ADDC
• The diagonals BD and AC are perpendicularly
  concurrent,i.e. ltBOAltBOCltDOAltDOC900

7
6. TRAPEZOIDA trapezoid is a quadrilateral that
has one pair of parallel sides.

• Properties of the trapezoid
• BC//AD
• Many kinds of the trapezoid
• 1. Isosceles trapezoid
• 2. A right trapezoid.

• Formula
• K ABBCCDDA
• L (AB DC). ½ t