Quadrilateral and other Polygons
• A polygon is a closed geometric figure, made up of line segments. The line segments are called sides and the end points of lines are called vertices(plural of vertex). Lines, inside the polygon, drawn from one vertex to the other, are called diagonals.
• The sum of the measures of the n angles in a polygon with n sides is always
( n - 2) × 180°.
• In any quadrilateral, the sum of the measures of the four angles is 360°
• A regular polygon is a polygon in which all of the sides are of the same length. In any regular polygon, the measure of each interior angle is
( n - 2) × 180°/ n and the measure of each exterior angle is
360°/n.
• A parallelogram is a special quadrilateral, in which both pairs of opposite sides are parallel. The Following are
some properties of parallelogram.
o Lengths of opposite sides are equal.
AB = CD and AD = BC
o Measures of opposite angles are equal.
a = c and b = d.
o Consecutive angles add up to 180°.
a + b = 180°, b + c = 180° etc.
o The two diagonals bisect each other. AE = EC and BE = ED
o A diagonal divides the parallelogram into two triangles that are congruent.
• A rectangle is a parallelogram in which all four angles are right angles. It has all the properties of a parallelogram. In addition it has the following
properties:
o The measure of each angle in a rectangle is 90°.
o The diagonals of a rectangle are equal in length.
• A square is a rectangle that has the following additional
properties:
o A square has all its sides equal in length.
o In a square, diagonals are perpendicular to each other.
• To calculate the area, the following formulas are required:
o For a parallelogram,
Area = bh, where
b is the base and
h is the height.
o For a rectangle,
Area = lw, where
l is the length and
w is the width.
o For a square, Area = s.s , where s is the side of the square.
• Perimeter for any polygon is the sum of lengths, of all its sides.
Continued...