Understanding quadrilaterals

UNDERSTANDING

QUADRILATERALS.

What is a quadrilateral? It is a 4-sided polygon, which is made up

entirely of line segments. Quadrilaterals can be divided into 5 types

i.e.., square, rectangle, rhombus, trapezium, parallelogram.

INTRODUCTION

QUADRILATERALS

Polygons with 4 sidesand 4 angles

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2

3

41 2

34

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2

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4

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4

Square Parallelogram Rectangle Trapezoid Rhombus

TYPES OF QUADRILATERALS

Hmmm. They are different shapes, yet they all have 4 sides…

A quadrilateral is a polygon with four sides.

A quadrilateral is named by its vertices.

QUADRILATERAL

It is a quadrilateral having all sides equal. All the angles are 90 degrees. The diagonals are equal and bisect each

other perpendicularly. The angle-sum property is 360 degrees.

SQUARE

How are they different?

SQUARE4 congruent sides

4 congruent angles

( Square = opposite of cool.)

It is a 4-side polygon having opposite sides equal.

Diagonals are equal and bisect each other Angle-sum property is 360 degrees. All the angles are 90 degrees.

RECTANGLE

In this polygon, only one pair of opposite sides are equal.

Diagonals are unequal

Trapezium

How are they different?

TRAPEZOIDOnly 1 pair of parallel sides

The trapezoid is usually the funkiest looking

quadrilateral.

It is a 4-sided polygon having opposites sides of equal length.

Diagonals are equal and bisect each other. Angle-sum property is 360 degrees.

PARALLELLOGRAM

How are they different?

PARALLELOGRAM2 pairs of parallel sides

Opposite sides congruent

Opposite angles congruent

It is a 4-sided polygon with all side equal. Diagonals are equal and bisect each other

perpendicularly. All sides are 90 degrees. Angle-sum property is 360 degrees.

RHOMBUS

How are they different?

RHOMBUSA parallelogram with 4 congruent (equal) sides

In figure A, the quadrilateral is named PQRS or QRSP or RSPQ or SPQR.

The order of the vertices is important. In figure B, the quadrilateral is named

MNOP. In figure C, the quadrilateral is named

DEFG.

A B C

P

Q R

S

M

N

O

P

D E

FG

In quadrilateral ABCD, the vertices are A, B,C, and D. Vertices A and B, B and C, C and D, D and A are consecutives vertices. Vertices A and C, B and D are opposite vertices. D

A

B

CD

Two sides with common vertex, like AB and BC, are consecutive sides. AB and DC, AD and BC, on the other hand are opposite hand.

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B

C

D

Two angles with a common side, like <A and <D, are consecutive angles.

<A and <C, <B and <D on the other hand are opposite angles.

AB

C

D

A

D

B

C

Segments joining opposite vertices like AC and BD are called diagonals of the quadrilateral.

Convex quadrilateral QRST, QS and RT intersect.

Nonconvex quadrilateral MNOP, MO and NP do not intersect.

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Q

RS

M

NO

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MADE BY: KONDET YASHWANT

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