3. QUADRILATERALS
A 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
4. 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 .
5. THEOREMS
i. Parallelograms have –
opposite sides equal.
opposite angles equal.
each diagonal bisects the parallelogram .
ii. Diagonals of a parallelogram bisect
each other.
6. 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 bisecteach other thenthe
quadrilateral is a parallelogram.
iv. A quadrilateral is a parallelogram, if its one pair of opposite sides are
equal andparallel.
7. 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.
8. 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.
9. 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.
