QUADRILATERALS
SOME IMPORTANT POINTS TO REMEMBER
·
"quadri-----
means four" and " lateral ----- means sides".
·
Quadrilateral
is a closed figure bounded by four sides such that no two line segments cross
each other.
·
The
sum of the angles of a quadrilateral is 360°.
·
A
quadrilateral having exactly one pair of parallel sides, is called a trapezium.
·
A
quadrilateral in which both pairs of opposite sides are parallel, is called a
parallelogram.
·
A
rectangle is a parallelogram whose angles are right angles.
·
A
rhombus is a parallelogram, whose all sides are equal.
·
A
square is a parallelogram whose all angles are right angles and all sides are
equal.
·
A
quadrilateral is a parallelogram , if
i. its opposite sides are equal;
ii. its opposite angles
are equal;
iii. its diagonals bisect
each other;
iv. it has one pair of
opposite sides equal and parallel.
·
In
a parallelogram
i. Diagonals divide it
into congruent triangles;
ii. Opposite sides are
equal;
iii. Opposite angles are
equal;
iv. The diagonals bisect
each other.
·
Diagonals
of a rectangle bisect each other and are equal and vice-versa.
·
Diagonals
of a rhombus bisect each other at right angles and vice -versa.
·
Diagonals
of a square bisect each other at right angles and are equal , and vice- versa.
·
The
line - segment joining the mid-points of any two sides of a triangle is
parallel to the third side and is half of it.
·
A
line through the mid -point of a side of a triangle parallel to another side
bisects the third side.
·
The
quadrilateral formed by joining the mid -points of the sides of a
quadrilateral, in order, is a parallelogram.
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