MATHS PRESENTATION
Aug 12, 2015
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