Category : 9th Class

FUNDAMENTALS

• Quadrilateral is a figure which is bounded by four straight lines. A quadrilateral has four vertices, four sides, four angles and sum of angles is${{360}^{{}^\circ }}$.

• Square:-

A quadrilateral which sides are equal and each angle is equal to ${{90}^{{}^\circ }}$ is called square.

Diagonals of square are equal and cut each other at${{90}^{{}^\circ }}$.

i.e., $AB=BC=CD=DA$.

$\angle A=\angle B=\angle C=\angle D$

and $AC=CD$.

• Rectangle

A quadrilateral whose all angles arc right angle and. each pair of opposite sides are equal is called Rectangle.

i.e., $\angle A=\angle \mathbf{B}=\angle C=\angle D={{90}^{{}^\circ }}$, and $AB=CD,AD=BC$ The diagonals of rectangle are equal and bisect each other at right angle. Each diagonal divides rectangle into congruent triangles.

i.e., $AC=BD$ and $\Delta ADC=\Delta ABC$, $\Delta ABD=\Delta BCD$

• Trapezium: A, quadrilateral in which exactly one pair of parallel sides are equal is called a trapezium

$AB\parallel CD$

• A trapezium, is an isosceles trapezium if its non - parallel sides are equal.
• ABCD is a isosceles trapezium if

$AB\parallel CD\text{ }and\text{ }AD=BC$.

• Parallelogram:- A quadrilateral having both pairs of opposite sides are equal is called a. parallelogram,

• In parallelogram ABCD $AB\parallel CD$ and $AD=BC$,
• In a parallelogram two opposite sides are equal.

i.e., $AD=BC,AB=CD$

• In a. parallelogram two opposite angles are equal

i.e., $\angle A=\angle C$ and $\angle B=\angle D$.

• In a parallelogram sum of two adjacent angles is ${{180}^{{}^\circ }}$e., $\angle A+\angle B={{180}^{{}^\circ }},\angle B+\angle C={{180}^{{}^\circ }}$

$\angle C+\angle D={{180}^{{}^\circ }}$and $\angle D+\angle A={{180}^{{}^\circ }}$

• Each diagonal of a parallelogram divides it into two congruent triangles.

i.e., $\Delta ABC=\Delta ADC$

$\Delta ABD=\Delta BCD$

• Rhombus:- A quadrilateral which all sides are equal is called a rhombus.

• The opposite side of a rhombus are parallel.

i.e., $AB\parallel CD$and $BC\parallel 2AD$

• Opposite angles of a rhombus are equal

i.e., $\angle A=\angle C$ and $\angle B=\angle D$

• Each diagonal of a rhombus divides it into two congruent triangles.