Quadrilaterals And Its Types
Quadrilateral: A closed figure having four sides, four angles and four vertices.
Parallelogram: A quadrilateral in which, opposite sides are parallel and equal, opposite angles are equal, the diagonals bisects each other, each diagonal divides parallelogram into two congruent triangles and adjacent angles are supplementary.
Square: A parallelogram in which, all the sides are equal, diagonals are equal and perpendicular bisector and each diagonal divides a square into two congruent triangles.
Rectangle: A parallelogram in which, diagonals are equal and bisects each other, and each diagonal divides rectangle into two congruent triangles.
Rhombus: a parallelogram in which, all the sides are equal, diagonals are perpendicular bisector and diagonal bisect the angle though which they pass.
Trapezium: a quadrilateral in which one pair of opposite sides is parallel.
A trapezium having non-parallel sides equal and base angles are equal is known as an isosceles trapezium.
Kite: A quadrilateral in which two pairs of adjacent sides are equal in length, one pair of opposite angles (the ones that are between the sides of unequal length) are equal in size, one diagonal bisects the other and diagonals intersect at right angles.
* The sum of four angles of quadrilateral is 360°.
Properties of a Parallelogram
* A quadrilateral is a closed figure which has four sides, four angles and four vertices.
A parallelogram is a quadrilateral in which
* Opposite sides are parallel and equal,
* Opposite angles are equal,
* The diagonals bisects each other,
* Each diagonal divides it into two congruent triangles,
* Adjacent angles are supplementary.
A square is a parallelogram in which
* All sides are equal,
* Each angle measure 90°,
* Diagonals are equal and bisect at right angles.
A rectangle is a parallelogram in which
* Diagonals are equal and bisect each other,
* Each angle measures 90°.
A rhombus is a parallelogram in which
* All four sides are equal,
* Diagonal bisects each other at right angles.
The Mid-Point Theorem
Mid-point theorem: The line segment joining the mid-points of two sides of a triangle is parallel to the third side and equal to half the third side.
Converse of Mid-point Theorem: The line drawn through the midpoint of one side of a triangle and parallel to another side bisects the third side.