quadrilaterals & paralleograms
TRANSCRIPT
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MATHS PRESENTATIO
N
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QUADRILATERALS AND
PARALLELOGRAMS
CHAPTER-9
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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
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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 .
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THEOREMS
i.Parallelograms have –
opposite sides equal.
opposite angles equal.
each diagonal bisects the parallelogram .
ii. Diagonals of a parallelogram bisect each
other.
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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.
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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.
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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.
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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.
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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.
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THANKYOU
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GUIDED BY:Mr. Jay Kumar
PRESENTED BY:Gargie DasIX ‘A’Roll- 08