- Quadrilateral
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- Parallelogram
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- Trapezium
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- Rhombus
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- Rectangle
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- Square
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- Mid-point Theorem for Triangles
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- How to solve the angle Problem in Quadilateral
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- Additional Topics

For ABCD to be quadrilateral, following condition are required

a) The four points A, B, C and D must be distinct and co-planar.

b) No three of points A, B, C and D are co-linear.

c) Line segments i.e. AB, BC, CD, DA intersect at their end points only.

1)AB, BC, CD and DA are the four sides.

2)Points A, B, C and D are the four vertices.

3)?ABC, ?BCD, ?CDA and ?DAC are the four angles.

4) AB and CD are the opposite sides.

5) Angle A and C are the opposite angles.

6) AB and BC are the adjacent sides.

7) Angle A and B are the adjacent angles

1) Sum of all the interior angles is 360

2) Sum of all the exterior angles is 360

Its properties are:

(a) The opposite sides of a parallelogram are equal.

(b) The opposite angles of a parallelogram are equal.

(c) The diagonals of a parallelogram bisect each other.

(d) The diagonal of a parallelogram divide into two congruent triangles

A quadrilateral is said to a parallelogram if

Opposite sides are equal OR Opposite angles are equal OR Diagonal bisects each other OR A pair of opposite are parallel and equal

Opposite sides are equal OR Opposite angles are equal OR Diagonal bisects each other OR A pair of opposite are parallel and equal

(a)All sides of a rhombus are equal

(b)The opposite angles of a rhombus are equal

(c)The diagonals of a rhombus bisect each other at right angles.

(a)The opposite sides of a rectangle are equal

(b) Each angle of a rectangle is a right-angle.

(c) The diagonals of a rectangle are equal.

(d) The diagonals of a rectangle bisect each other.

(a)All the sides of a square are equal.

(b) Each of the angles measures 90°.

(c) The diagonals of a square bisect each other at right angles.

(d) The diagonals of a square are equal.

All the quadrilaterals can be shown in Venn diagram like this

We can divide the entire set of quadilateral in three major parts

1) general quadrilaterals

2)parallelograms

3) trapezoids.

a) A square is always a parallelogram Similary a rectangle is always a parallelogram

b) A square is always a rectangle,rhombus

c) A rhombus can be square.

d) A rectangle has four right angles.

e) A rectangle is not always a rhombus

f) A Trapezium is not a parallelogram

The line segment joining the mid points of the two sides of the triangle is parallel to the third side

A line drawn through mid point of one side of a triangle and parallel to another side bisect the third side of the triangle

1) We will be given problem where three angles of quadilateral known or two angles are known with other two angles having some relationship

2) Case1 : Three angles are known,How to find the fourth angle

As per angle property of quadilateral

Sum of all the interior angles is 360

So

A+B+C+D=360

If A,B,C are known we can find D easily

3) case 2:two angles are known with other two angles having some relationship

A and B are known and 2C-D= 50

Now again we know that

A+B+C+D=360

Then C+D=

We can find the values of C and D from below two equations

2C-D= 50

C+D=

Example 1:The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral

Solution:

Angles are 3x,5x,9x,13x

So

3x+5x+9x+13x=360

30x=360

x=12

So angles are

36, 60,108, 156

Solution:

Angles are 3x,5x,9x,13x

So

3x+5x+9x+13x=360

30x=360

x=12

So angles are

36, 60,108, 156

1) Quadilateral meams Quad( Four ) ,Lateral means sides

2) A quadrilateral is also sometimes called Quadrangle ("four angles"), so it sounds like "triangle"

or Tetragon ("four and polygon"), so it sounds like "pentagon", "hexagon", etc.

3) Quadilaterals can be classified in terms of parallel pair of lines also

No Pair of Parallel lines: General quadilaterals

One pair of parallel lines: Trapezium

Two pair of parallel lines : square,parallelogram,rectangle,rhombus

All sides congurent: Square,rhombus

One pair of sides are congurent:Isococeles Trapezium

Two pair of sides are congurent: Rectangle,parallelogram,Kite

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