Quadrilaterals & Parallelograms

MATHS PRESENTATIO

N

QUADRILATERALS AND

PARALLELOGRAMS

CHAPTER-9

QUADRILATERALSA plane figure bounded by four line segments AB, BC, CD and DA

is

called a quadrilateral, written as ABCD or, ABCD. D C

A B

TYPES OF QUADRILATERALS

PARALLELOGRAM- A quadrilateral in which opposite sides are

parallel is called parallelogram .

RECTANGLE- A parallelogram each of whose angle is 90 , is

called a rectangle, written as rect. ABCD, etc.

SQUARE- A rectangle having all sides equal is called a rhombus

.

TRAPEZIUM- A quadrilateral in which two opposite sides are

parallel and two opposite sides are non-parallel , is called a

trapezium .

THEOREMS

i.Parallelograms have –

opposite sides equal.

opposite angles equal.

each diagonal bisects the parallelogram .

ii. Diagonals of a parallelogram bisect each

other.

CONVERSE OF THE ABOVE THEOREMS

i.A quadrilateral is a parallelogram, if its opposite

sides are equal.

ii.A quadrilateral is a parallelogram, if its opposite

angles are equal.

iii. If the diagonals of a quadrilateral bisect each

other then the quadrilateral is a parallelogram.

iv.A quadrilateral is a parallelogram, if its one pair

of opposite sides are equal and parallel.

THEOREMS

1.Diagonals of a rectangle are equal.

2.Diagonals of a rhombus are

perpendicular to each other.

3.Diagonals of a square are equal and

perpendicular to each other.

CONVERSE OF THE ABOVE THEOREMS

1.If the two diagonals of a parallelogram are equal,

then the parallelogram is a rectangle.

2.If the diagonals of a parallelogram are

perpendicular to each other, then it is a rhombus.

3.If the diagonals of a parallelogram are equal and

intersect at right angles then the parallelogram

is a square.

INTERCEPT THEOREM

If there are three lines and the

intercepts made by them on one

transversal are equal then the

intercepts on any other transversal are

also equal.

MIDPOINT THEOREM

The line segment joining

the midpoints of any two

sides of a triangle is

parallel to the third side

and equal to half of it.

THANKYOU

GUIDED BY:Mr. Jay Kumar

PRESENTED BY:Gargie DasIX ‘A’Roll- 08