Types of Quadrilaterals

Class – 9 (A)

Submitted to – D.N Soni Sir

P.p.t Made By -Raksha

Sharma

Square: Quadrilateral with four equal sides and four right angles (90 degrees)

Indicates equal sides

Box indicates 900 angle

Types of Quadrilaterals


Rectangle: Quadrilateral with two pairs of equal sides and four right angles (90 degrees)


Box indicates 900 angle


Parallelogram: Quadrilateral with opposite sides that are parallel and of equal length and opposite angles are equal



Rhombus: Parallelogram with four equal sides and opposite angles equal



Trapezoid: Quadrilateral with one pair of parallel sides

Parallel sides never meet.


Irregular shapes: Quadrilateral with no equal sides and no equal angles

Name the Quadrilaterals

1 2 3

4 5 6

rectangle irregular rhombus

parallelogram trapezoid square

Interior Angles

Interior angles: An interior angle (or internal angle) is an angle formed by two sides of a simple polygon that share an endpoint

Interior angles of a quadrilateral always equal 360 degrees

A diagonal of a parallelogram divides it into two congruent triangles.In a parallelogram ,opposite sides are equal.

If each pair of opposite sides of quadrilateral is equal then it is a parallelogram.In a parallelogram opposite angles are equal.

If in a quadrilateral each pair of opposite angles is equal then it is a parallelogram. The diagonals of a parallelogram bisect each other.

If the diagonals of a quadrilateral bisect each other then it is a parallelogram.

We have studied many properties of a parallelogram in this chapter and we have also verified that if in a quadrilateral any one of those properties is satisfied, then it becomes a parallelogram. There is yet another condition for a quadrilateral to be a parallelogram.It is stated as follows:

A QUDRILATERAL IS A PARALLELOGRAM IF A PAIR OF OPPOSITE SIDES IS EQUAL AND PARALLEL.

A

Q C

P B

D

S R

Example: ABCD is a parallelogram in which P and Q are mid points of opposite sides AB and CD. If AQ intersects DP at S and BQ intersects CP at R, show that:

1. APCQ is a parallelogram2. DPBQ is a parallelogram3. PSQR is a parallelogram SOLUTION: 1. In quadrilateral APCQ,

AP is parallel to QC AP = ½ AB , CQ = ½ CD , AB = CD, AP = CQTherefore APCQ is a parallelogram. (theorem 8.8) 2.Similarly quadrilateral DPBQ is a parallelogram because DQ is parallel to PB and DQ = PB3. In quadrilateral PSQR SP is parallel to QR and SQ is parallel to PR.SO ,PSQR is a parallelogram.

What is the sum of angles in triangle ADC?

D C

BAWe know that angle DAC+ angle ACD+ angle D = 180

Similarly in triangle ABC, angle CAB + angle ACB + angle B = 180

Adding 1 and 2 we get , angles DAC + ACD + D + CAB + ACB + B =180 + 180 = 360

Also, angles DAC + CAB = angle A and angle ACD + angle ACB = angle C So, angle A + angle D +angle B + angle C = 360i.e. THE SUM OF THE ANGLES OF A QUADRILATERAL IS 360.

Angle Sum Property Of a Quadrilateral

Education

Types of Quadrilaterals