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# Types of Quadrilaterals and Their Properties(With Definitions & Examples)

December 16, 2022

This post is also available in: हिन्दी (Hindi)

A quadrilateral is a closed shape and a type of polygon that is formed by four non-colinear points having four sides, four vertices, and four angles. There are various types of quadrilaterals based on their properties. Squares, rectangles, parallelograms, and rhombus are a few types of quadrilaterals.

Let’s learn about different types of quadrilaterals and their properties with their examples.

In concave quadrilaterals, one interior angle is greater than $180^{\circ}$. A quadrilateral is called a concave quadrilateral if at least one diagonal, i.e. the line segment joining the vertices is not a part of the same region of the quadrilateral.

In convex quadrilaterals, each interior angle is less than $180^{\circ}$. A quadrilateral is convex if both diagonals lie in the same region of the quadrilateral.

The convex quadrilaterals are further divided into six types. These six types of quadrilaterals are

• Parallelogram
• Trapezium
• Rhombus
• Rectangle
• Square
• Kite

Let’s learn about these in detail.

### Parallelogram

A quadrilateral in which the opposite sides are parallel to each other and equal in length is called a parallelogram. The sum of its consecutive angles in a parallelogram is equal to $180^{\circ}$. The diagonals of a parallelogram intersect each other at the midpoint.

Examples of a parallelogram are the flat surfaces of tables, desks, etc.

The following are some of the properties of parallelograms.

• Two pairs of parallel sides
• Opposite sides of equal lengths
• Opposite angles that are equal
• Two diagonals bisect each other, i.e., one diagonal divides the other diagonal into exactly two halves.

In the above figure, $\text{ABCD}$ is a parallelogram, where $\text{AB} || \text{CD}$ and $\text{BC} || \text{DA}$. The diagonals intersect at the middle point $\text{O}$ where $\text{AO} =$\text{OC}$and$\text{BO}$=$\text{OD}$. In mensuration, a parallelogram has two types of measurements. • Perimeter of Parallelogram • Area of a Parallelogram Is your child struggling with Maths? We can help! Country • Afghanistan 93 • Albania 355 • Algeria 213 • American Samoa 1-684 • Andorra 376 • Angola 244 • Anguilla 1-264 • Antarctica 672 • Antigua & Barbuda 1-268 • Argentina 54 • Armenia 374 • Aruba 297 • Australia 61 • Austria 43 • Azerbaijan 994 • Bahamas 1-242 • Bahrain 973 • Bangladesh 880 • Barbados 1-246 • Belarus 375 • Belgium 32 • Belize 501 • Benin 229 • Bermuda 1-441 • Bhutan 975 • Bolivia 591 • Bosnia 387 • Botswana 267 • Bouvet Island 47 • Brazil 55 • British Indian Ocean Territory 246 • British Virgin Islands 1-284 • Brunei 673 • Bulgaria 359 • Burkina Faso 226 • Burundi 257 • Cambodia 855 • Cameroon 237 • Canada 1 • Cape Verde 238 • Caribbean Netherlands 599 • Cayman Islands 1-345 • Central African Republic 236 • Chad 235 • Chile 56 • China 86 • Christmas Island 61 • Cocos (Keeling) Islands 61 • Colombia 57 • Comoros 269 • Congo - Brazzaville 242 • Congo - Kinshasa 243 • Cook Islands 682 • Costa Rica 506 • Croatia 385 • Cuba 53 • Cyprus 357 • Czech Republic 420 • Denmark 45 • Djibouti 253 • Dominica 1-767 • Ecuador 593 • Egypt 20 • El Salvador 503 • Equatorial Guinea 240 • Eritrea 291 • Estonia 372 • Ethiopia 251 • Falkland Islands 500 • Faroe Islands 298 • Fiji 679 • Finland 358 • France 33 • French Guiana 594 • French Polynesia 689 • French Southern Territories 262 • Gabon 241 • Gambia 220 • Georgia 995 • Germany 49 • Ghana 233 • Gibraltar 350 • Greece 30 • Greenland 299 • Grenada 1-473 • Guadeloupe 590 • Guam 1-671 • Guatemala 502 • Guernsey 44 • Guinea 224 • Guinea-Bissau 245 • Guyana 592 • Haiti 509 • Heard & McDonald Islands 672 • Honduras 504 • Hong Kong 852 • Hungary 36 • Iceland 354 • India 91 • Indonesia 62 • Iran 98 • Iraq 964 • Ireland 353 • Isle of Man 44 • Israel 972 • Italy 39 • Jamaica 1-876 • Japan 81 • Jersey 44 • Jordan 962 • Kazakhstan 7 • Kenya 254 • Kiribati 686 • Kuwait 965 • Kyrgyzstan 996 • Laos 856 • Latvia 371 • Lebanon 961 • Lesotho 266 • Liberia 231 • Libya 218 • Liechtenstein 423 • Lithuania 370 • Luxembourg 352 • Macau 853 • Macedonia 389 • Madagascar 261 • Malawi 265 • Malaysia 60 • Maldives 960 • Mali 223 • Malta 356 • Marshall Islands 692 • Martinique 596 • Mauritania 222 • Mauritius 230 • Mayotte 262 • Mexico 52 • Micronesia 691 • Moldova 373 • Monaco 377 • Mongolia 976 • Montenegro 382 • Montserrat 1-664 • Morocco 212 • Mozambique 258 • Myanmar 95 • Namibia 264 • Nauru 674 • Nepal 977 • Netherlands 31 • New Caledonia 687 • New Zealand 64 • Nicaragua 505 • Niger 227 • Nigeria 234 • Niue 683 • Norfolk Island 672 • North Korea 850 • Northern Mariana Islands 1-670 • Norway 47 • Oman 968 • Pakistan 92 • Palau 680 • Palestine 970 • Panama 507 • Papua New Guinea 675 • Paraguay 595 • Peru 51 • Philippines 63 • Pitcairn Islands 870 • Poland 48 • Portugal 351 • Puerto Rico 1 • Qatar 974 • Romania 40 • Russia 7 • Rwanda 250 • RÃ©union 262 • Samoa 685 • San Marino 378 • Saudi Arabia 966 • Senegal 221 • Serbia 381 p • Seychelles 248 • Sierra Leone 232 • Singapore 65 • Slovakia 421 • Slovenia 386 • Solomon Islands 677 • Somalia 252 • South Africa 27 • South Georgia & South Sandwich Islands 500 • South Korea 82 • South Sudan 211 • Spain 34 • Sri Lanka 94 • Sudan 249 • Suriname 597 • Svalbard & Jan Mayen 47 • Swaziland 268 • Sweden 46 • Switzerland 41 • Syria 963 • Sao Tome and Principe 239 • Taiwan 886 • Tajikistan 992 • Tanzania 255 • Thailand 66 • Timor-Leste 670 • Togo 228 • Tokelau 690 • Tonga 676 • Trinidad & Tobago 1-868 • Tunisia 216 • Turkey 90 • Turkmenistan 993 • Turks & Caicos Islands 1-649 • Tuvalu 688 • U.S. Outlying Islands • U.S. Virgin Islands 1-340 • UK 44 • US 1 • Uganda 256 • Ukraine 380 • United Arab Emirates 971 • Uruguay 598 • Uzbekistan 998 • Vanuatu 678 • Vatican City 39-06 • Venezuela 58 • Vietnam 84 • Wallis & Futuna 681 • Western Sahara 212 • Yemen 967 • Zambia 260 • Zimbabwe 263 Age Of Your Child • Less Than 6 Years • 6 To 10 Years • 11 To 16 Years • Greater Than 16 Years ### Trapezium A quadrilateral in which one pair of opposite sides parallel, is called a trapezium. In trapezium, two pairs out of four pairs of adjacent angles are supplementary. The sides that are parallel to each other are called bases and the sides that are not parallel to each other are called legs. Examples of a trapezium are drawings of bridges, handbags, etc. The following are some of the properties of trapezium. • One pair of opposite sides are parallel • The sum of two pairs of adjacent angles is$180^{\circ}$In the above figure,$\text{PQRS}$is a trapezium, where$\text{PQ} || \text{RS}$,$\angle \text{P} + \angle \text{S} = 180^{\circ}$, and$\angle \text{Q} + \angle \text{R} = 180^{\circ}$. In mensuration, a trapezium has two types of measurements. ### Rhombus A rhombus is also known as an equilateral quadrilateral or a diamond that has all four sides of equal lengths. In a rhombus, the opposite sides are parallel and the opposite angles are equal. Examples are the plane surfaces of mirrors, section-based football fields, etc. The following are the properties of a rhombus. • All four sides are equal in length • Opposite angles are equal • Diagonals are unequal and perpendicular to each other • The diagonals bisect each other • Opposite sides are equal and parallel In the above figure$\text{PQRS}$is rhombus, where$\text{PQ} || \text{RS}$and$\text{PS} || \text{QR}$. All the sides are equal to each other, i.e.,$\text{PQ} = \text{QR} = \text{RS} = \text{SP}$. In mensuration, a rhombus has two types of measurements. ### Rectangle In a rectangle opposite sides are of equal length and parallel to each other. The angles of a rectangle are equal in measure and are right-angled i.e. they measure$90^{\circ}$. Examples of a rectangle are dollar bills, a playing card, flat surface of a board, etc. The following are the properties of a rectangle. • Two pairs of parallel sides • All four angles are right angles, that is, they measure$90^{\circ}$• Opposite sides are of equal lengths • Two equal diagonals • The two diagonals bisect each other in equal halves In the above figure,$\text{ABCD}$is a rectangle where,$\text{AB} || \text{CD}$,$\text{AB} = \text{CD}$,$\text{BC} || \text{DA}$, and$\text{BC} = \text{DA}$. All the angles are$90^{\circ}$, i.e.,$\angle \text{A} = \angle \text{B} = \angle \text{C} = \angle \text{D} = 90^{\circ}$. In mensuration, a rectangle has two types of measurements. ### Square In a square, all sides are equal in length and all angles are of equal measure, which$90^{\circ}$each. An example of a square is a chessboard. The following are the properties of a square. • All sides are equal in length • All four internal angles measure$90^{\circ}$• Diagonals are equal and perpendicular to each other In the above figure$\text{PQRS}$is a square, where$\text{PQ} = \text{QR} = \text{RS} = \text{SP}$, and$\text{PQ} || \text{RS}$and$\text{PS} || \text{QR}$. All the angles are$90^{\circ}$, i.e.,$\angle \text{P} = \angle \text{Q} = \angle \text{R} = \angle \text{S} = 90^{\circ}$. In mensuration, a square has two types of measurements. ### Kite A kite has two pairs of adjacent sides are of equal length. A kite is also called a dart or an arrowhead because of its shape. A real-life example is a kite itself. The following are the properties of a kite. • Two pairs of adjacent sides equal • Diagonals are perpendicular to each other In the above figure$\text{ABCD}$is a kite where,$\text{AB} = \text{DA}$, and$\text{BC} = \text{CD}\$.

In mensuration, a kite has two types of measurements.

## Practice Problems

1. What is a convex quadrilateral?
2. What is a concave quadrilateral?
3. Write down the important properties of
• Parallelogram
• Trapezium
• Rhombus
• Rectangle
• Square
• Kite

## FAQs

### What are the 6 types of quadrilaterals?

The 6 types of quadrilaterals are parallelogram, trapezium, rhombus, rectangle, square, and kite.

### Which quadrilateral has four congruent sides?

The quadrilaterals having all four sides congruent are square and rhombus.

### What kind of quadrilateral has 4 equal sides and 4 right angles?

A quadrilateral that has 4 equal sides and 4 right angles is a square.

### Do kites have parallel sides?

No, there are no parallel sides for a kite.

## Conclusion

The quadrilaterals are broadly categorized as concave and convex quadrilaterals. The convex quadrilaterals are further divided into six types, each having its own unique shape and properties. The six types of quadrilaterals are parallelogram, trapezium, rhombus, rectangle, square, and kite.