A quadrilateral is a 2-dimensional closed shape with four straight sides. E.g. The shape ABCD shown here is a quadrilateral.

A line segment drawn from one vertex of a quadrilateral to the opposite vertex is called a diagonal of the quadrilateral. AC is a diagonal of quadrilateral ABCD, so is BD.

TYPES & PROPERTIES OF QUADRILATERALS

There are seven types of quadrilaterals that can be divided into two groups: parallelograms and other quadrilaterals.

1. Parallelograms

Quadrilaterals are called parallelograms if both pairs of opposite sides are equal and parallel to each other. Different parallelograms and their properties.

a) Parallelogram
Opposite sides of a parallelogram are parallel and equal in length. Opposite angles are equal in size.

b) Rectangle
Opposite sides of a rectangle are parallel and equal in length, All angles are equal to 90°.

c) Square
Opposite sides of a square are parallel and all sides are equal in length, All angles are equal to 90°.

d) Rhombus
All sides of a rhombus are equal in length,
Opposite sides are parallel,
Opposite angles of a rhombus are equal,
The diagonals of a rhombus bisect each other at right angles.

Rectangles, squares and rhombuses are parallelograms.

2.Other Quadrilaterals

Other quadrilaterals include trapeziums, kites and irregular quadrilaterals.

a) Trapezium
A trapezium has one pair of opposite sides parallel.
A regular trapezium has non-parallel sides equal and its base angles are equal.

b) Kite
Two pairs of adjacent sides of a kite are equal in length
One pair of opposite angles are equal in size.
One diagonal bisects the other.
Diagonals intersect at right angles.

3. Irregular Quadrilateral

An irregular quadrilateral does not have any special properties.

...QUADRILAERALS
QUADRILATERALS – Quadrilateral is a union of four line segments determined by four distinct co-planar points of which no three are collinear and the line-segment intersect at end points.
Quadrilateral ABCD is denoted by □ABCD.
PARTS OF QUADRILATERAL: (□ABCD)
Points A, B, C, D are called the vertices of □ABCD
AB, BC, CD and AD are called the sides of ABCD
AC, BD are called Diagonals of ABCD
A, B,C and D are the four angles of ABCD
A Quadrilateral has 10 parts – 4 line segments, 4 angles, 2 diagonals.
Sides of Quadrilateral are the subset of Quadrilateral.
Angels of Quadrilateral are not a subset of a Quadrilateral.
Diagonals of a Quadrilateral are not a subset of Quadrilateral.
ADJACENT SIDES: Two sides of a Quadrilateral intersecting in a vertex are called adjacent sides. E.g- AB and BC, BC and CD, CD and DA, DA and AB.
OPPOSITESIDES: The sides of a Quadrilateral with no common end point are called oppositesides. E.g- AB and CD, AD and BC.
The intersection of oppositesides is null set.
ADJACENT ANGLES: A and B, B and C, C and D, D and A...

...Quadrilaterals
*4 sides
* Sum of interior and exterior angles is 360®
Parallelogram
Kite
Trapezoid
1. Oppositesides are parallel
1. Two pairs of consecutive sides congruent
1. One pair of parallel sides
2. Oppositesides are congruent
2. Diagonals are perpendicular
2. Consecutive angles are
supplementary
3. Opposite angles are congruent
3. One pair of opposite angles are congruent
4. Consecutive angles are supplementary
4. Shorter diagonal is bisected
Isosceles Trapezoid
5. Diagonals bisect each other
Rhombus
Rectangle
1. Four congruent sides
1. Four right angles
2. Diagonals are perpendicular
2. Diagonals are congruent
Square
All of the above (12)
3. Diagonals bisect opposite
angles (vertices)
1. Base angles are
congruent
2. Diagonals are congruent
3. Legs of trapezoid are
congruent
...

...Class IX (Term 2) 8. QUADRILATERALS
IMPORTANT TERMS, DEFINITIONS AND RESULTS
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Sum of the angles of a quadrilateral is 360°. A diagonal of a parallelogram divides it into two congruent triangles. In a parallelogram, (i) oppositesides are equal (ii) opposite angles are equal (iii) diagonals bisect each other A quadrilateral is a parallelogram, if (i)oppositesides are equal or (ii) opposite angles are equal or (iii) diagonals bisect each other or (iv) a pair of oppositesides is equal and parallel
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Diagonals of a rectangle bisect each other and are equal and vice-versa. Diagonals of a rhombus bisect each other at right angles and vice-versa. Diagonals of a square bisect each other at right angles and are equal, and vice-versa. The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is half of it. A line through the mid-point of a side of a triangle parallel to another side bisects the third side. The quadrilateral formed by joining the mid-points of the sides of a quadrilateral, in order, is a parallelogram.
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SUMMATIVE ASSESSMENT MULTIPLE CHOICE QUESTIONS
PR...

...to develop critical and analytical skills.
The quadrilateral is a very interesting concept for it is rich in content and applications. Quadrilaterals such as the golden rectangle and cyclic quadrilateral are famous for their intricate properties. In high schools, however, this concept is not given emphasis and teachers are confined within the types of quadrilaterals enumerated in the textbook. In effect, students’ learning is shallow. Their interests are not stimulated and they think quadrilaterals are very simple. But when given problems on quadrilaterals that are of moderate difficulty, they are stumped.
1.2 Statement of the Problem
The aims of this paper are to define circumscribable quadrilaterals and to present the proofs of its properties. It also intends to discuss and prove the conditions for a quadrilateral to be circumscribable.
This paper is inspired by Charles Worrall’s article entitled “ A Journey with Circumscribable Quadrilaterals” published in the Delving Deeper section of the Mathematics Teacher in October 2004. In the paper, the author explained the importance of inquiry in teaching and learning mathematics. He also emphasized creative thinking in order to better understand and appreciate the beauty of mathematics particularly geometry.
1.3 Scope and Limitation of the Study
Due to the limited time devoted in making...

...-------------------------------------------------
Golden Quadrilateral
From Wikipedia, the free encyclopedia
Golden Quadrilateral |
Highway map of India with the Golden Quadrilateral highlighted in solid blue colour |
Route information |
Maintained by NHAI |
Length: | 5,846 km (3,633 mi) |
Delhi – Kolkata |
Length: | 1,453 km (903 mi) |
Major
junctions: | NH 2 |
Delhi – Mumbai |
Length: | 1,419 km (882 mi) |
Major
junctions: | NH 8, NH 79A, NH 79, NH 76 |
Mumbai – Chennai |
Length: | 1,290 km (800 mi) |
Major
junctions: | NH 4, NH 7, NH 46 |
Kolkata – Chennai |
Length: | 1,684 km (1,046 mi) |
Major
junctions: | NH 6, NH 60, NH 5 |
Highway system |
* Indian Road Network * National * Expressways * State |
A section of the Golden Quadrilateral highway from Chennai – Mumbai phase
NH46: Bengaluru-Chennai section of India's 4-lane Golden Quadrilateral highway
NH5 - another section of India's GQ highway
NH6: Chennai-Kolkata section of the GQ highway
Kolkata-Delhi section of India's GQ highway
NH76: Delhi-Mumbai section of India's GQ highway
The Golden Quadrilateral is a highway network connecting India's four largest metropolises: Delhi, Mumbai, Kolkata and Chennai, thus forming a quadrilateral of sorts. Four other cities among the top ten metropolises: Bangalore, Pune, Ahmedabad, and Surat, are also served...

...Euthanasia
Euthanasia is a relatively touchy subject and everyone has their own opinion on it. For me, I am pro-euthanasia and I believe that an individual’s right to autonomy and freedom of choice, euthanasia should be legalized in all the states. It is only fair to give someone that right because death is a private matter and should not be controlled by others.
If a person autonomously chooses to end his or her life or have someone else assist them in doing so, it should be allowed. One should be free to do so as long as no harm is done to others. Moreland goes farther and gives an argument dealing with autonomy stating “Since biological life is not the real, moral issue, then life is not intrinsically valuable or sacred simply because it is human life.” He goes on saying that the more important aspect would be biological life, which deals with autonomy (Moreland).
There are many people who are stuck in hospital beds for months, even years, wired with tubes unable to move from where they lay. They slowly die in a long painful death unable to do anything, while family members watch in agony as their loved one withers away. What an undignified way to die, a slow painful death, too sad to watch. We can prevent this if euthanasia was in place. Euthanasia can quickly and humanely end a patients suffering allowing them to die with dignity (Euthanasia). Not only does this help patients die a more painless death, it also can help shorten the grief and suffering or the...

...[pic]
A parallelogram is a quadrilateral in which pairs of oppositesides are parallel and are congruent.
Oppositesides are parallel and equal in length, and opposite angles are equal (angles "a" are the same, and angles "b" are the same)
NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!
Name the kind of parallelogram this figure displays? Example 1: [pic]
|[pic] |A parallelogram with: |
| |all sides equal and |
| |angles "a" and "b" as right angles |
| |Is a square! |
Perimeter and area of a parallelogram
Perimeter of a parallelogram:
The perimeter can be calculated with the following formula:
[pic]
Where a and b are the side lengths.
Area of a parallelogram
The area can be calculated with the following formulas:
[pic]
Where b is the length of the base line, and h is the height of the parallelogram.
[pic]
Where a and b are the side lengths and θ is the angle.
[pic]...

...8th QUADRILATERAL AND PARALLELOGRAM
1. Prove that in a parallelogram, the oppositesides are equal and the
opposite angles are equal.
2. Prove that diagonals of a rhombus bisect each other at right
angles.
3. Two adjacent angles of a parallelogram are as 2:3. Find the
measure of each of its angles.
4. Prove that the diagonals of a square are equal and bisect each other
at right angles.
5. If an angle of a parallelogram is two-third of its adjacent angle,
then what is the smallest angle of the parallelogram?
6. The length of diagonals of a rhombus are 16cmand12cm. Find the
length of each side of the rhombus.
7. The length and breadth of a rectangle are in the ratio 4:3. If the
diagonals measures 25cm, then what is the perimeter of the
rectangle?
8. If one angle of a parallelogram is 24less than twice the smallest
angle, then what is the largest angle of the parallelogram?
www.jsuniltutorial.weebly.com/
Page 1
8th QUADRILATERAL AND PARALLELOGRAM
9. Prove that any two adjacent angles of a parallelogram are
supplementary.
10.
The sides of a rectangle are in the ratio 5:4and its perimeter is
90cm. Find its length and breadth.
11.
Prove that the sum of exterior angles of a quadrilateral is360
12....