In this lesson you’ll learn the Properties of different types of Quadrilaterals.
You’ll explore it starting from earlier learning about polygons.
The quadrilaterals always have 4 sides and in broad framework there are seven types
of quadrilaterals that may be divided into two major groups i.e. parallelograms
and other quadrilaterals. Also the interior angles of a quadrilateral add up to
360 degrees. The properties and related details will be explained in the contents
presented by the instructor in own handwriting, using video and
with the help of several examples with solution.
Properties of quadrilaterals: In a quadrilateral; if opposite sides and opposite angles are equal, it is a parallelogram.
Important Properties of parallelograms: In a parallelogram
• opposite sides are equal
• opposite angles are equal
• diagonals bisect each other (More text below video...)
Parallelogram: • Both pairs of opposite sides are parallel.
• Both pairs of opposite sides are congruent.
• One pair of opposite sides are parallel and congruent.
• Diagonals bisect each other.
• Both pairs of opposite angles are congruent.
• Consecutive angles are supplementary.
Square • It has all the properties of a parallelogram.
• It has all the properties of a rectangle.
• It has all the properties of a rhombus.
Rectangle
• It has all the properties of a parallelogram.
• It has a right angle.
• Diagonals are congruent.
Trapezoid
• In Trapezoid exactly one pair of opposite sides are parallel.
• In this exactly two pairs of consecutive angles are supplementary.
Rhombus • It has all the properties of a parallelogram.
• It has all sides are congruent.
• Here diagonals are perpendicular.
• Diagonals bisect the opposite angles.
Kite:
• In this both pairs of consecutive sides are congruent but opposite sides
are not congruent.
• It has perpendicular diagonals.
• Exactly one pair of opposite angles are congruent.
Now you can further explore and learn relationship in more details. For example,
Parallelogram:
Each pair of opposite sides is equal and parallel
In Fig1 below,
Opposite sides: PQ  SR and PS  QR
PQ = SR and PS = QR
Opposite angles are equal
In the Fig1
P
=
R and
Q=
S
Diagonals of a parallelogram bisect each other
In the Fig2, OS = OQ and OP = OR
Each diagonal divides the parallelogram into two congruent triangles i.e. in the
Fig2,
PQS
RSQ.
Similarly,
PQR
RSP
Opposite Sides Two sides of a quadrilateral, that have no common point, are known
as opposite sides. In Fig3, PQ and SR is one pair of opposite sides and PS and
QR is the other pair of opposite sides
Consecutive sides
Two sides of a quadrilateral, that have a common end point, are known
as consecutive sides. In Fig 3, PQ and QR is one pair of consecutive sides. Then
QR, RS; RS, SP; and SP, PQ are the other three pairs of consecutive sides
Opposite angles Two angles, that do not include a side in their intersection, are
known as the opposite angles of a quadrilateral. In the above figure, angle P and
angle R is one pair of opposite angles, Q and S is another pair of opposite angles.
Consecutive angles Two angles of a quadrilateral, which include a side in their intersection,
are called consecutive angles. In above figure, angle P and angle Q
is one pair of consecutive angles, Q,R; R,S; and S,P are the other three pairs of
consecutive angles.
Remembering the properties of quadrilaterals in above table and here below will
help you to apply them to solve the problems:
• A parallelogram is a quadrilateral whose opposite sides equal and parallel.
• A rectangle, a rhombus and a square are considered as parallelograms
• A trapezoid is quadrilateral with one pair of opposite sides being parallel. Thus,
it is not a parallelogram.
The video above will explain more in detail about Quadrilateral properties and
their relationship, with the help of several examples.
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