Maharashtra Board Class 9 Maths Part II Chapter 5 Quadrilaterals PDF Download

Quadrilaterals

Let's Recall

Write the following pairs considering ABCD.

Pairs of adjacent sides: (1) ... , ... (2) ... , ... (3) ... , ... (4) ... , ...

Pairs of adjacent angles: (1) ... , ... (2) ... , ... (3) ... , ... (4) ... , ...

Pairs of opposite sides: (1) ..... , ..... (2) ..... , .....

Pairs of opposite angles: (1) ..... , ..... (2) ..... , .....

Let's Recall Types Of Quadrilaterals And Their Properties

I am a quadrilateral.

My both pairs of opposite sides are parallel.

My all angles are right angles.

My all sides are equal in length.

My all angles are equal and all sides are equal.

My properties: Opposite sides congruent. Opposite angles ...... Diagonals .....

My properties: Opposite sides ..... Diagonals .....

My properties: Opposite sides ..... Diagonals .....

My properties: Diagonals .....

My only one pair of opposite sides is parallel.

Teacher's Note

A quadrilateral is a shape with four sides and four angles. You see quadrilaterals every day in windows, doors, and notebook pages.

Exam Trick

Remember: Parallelogram = opposite sides equal and parallel. Think of railway tracks going forward - both sides stay equal distance apart.

Points to Remember

A quadrilateral has four sides and four angles.
Opposite sides are sides that do not touch each other.
Adjacent sides are sides that touch at a corner.
A parallelogram has opposite sides that are parallel and equal.
Different quadrilaterals have different properties.

Let's Learn

Parallelogram

A quadrilateral having both pairs of opposite sides parallel is called a parallelogram.

For proving the theorems or for solving the problems we need to draw figure of a parallelogram frequently. Let us see how to draw a parallelogram.

Suppose we have to draw a parallelogram ABCD.

Method I

Let us draw seg AB and seg BC of any length and making an angle of any measure with each other.

Now we want seg AD and seg BC parallel to each other. So draw a line parallel to seg BC through the point A.

Similarly we will draw line parallel to AB through the point C. These lines will intersect in point D.

So constructed quadrilateral ABCD will be a parallelogram.

Method II

Let us draw seg AB and seg BC of any length and making angle of any measure between them.

Draw an arc with compass with centre A and radius BC.

Similarly draw an arc with centre C and radius AB intersecting the arc previously drawn.

Name the point of intersection of two arcs as D.

Draw seg AD and seg CD.

Quadrilateral so formed is a parallelogram ABCD.

Teacher's Note

You can draw a parallelogram by making two pairs of parallel lines. This is like drawing railway tracks on paper - two lines that never meet.

Exam Trick

To draw a parallelogram quickly, remember: Draw one side, then draw another side at any angle. Now draw two more sides parallel to the first two sides.

Points to Remember

A parallelogram has opposite sides that are parallel.
Opposite sides of a parallelogram are equal in length.
You can draw a parallelogram using a ruler and compass.
A parallelogram does not need to have right angles.
Many real objects have the shape of a parallelogram.

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