• Home
  • /
  • Blog
  • /
  • How to Construct Parallel Lines(With Steps & Examples)

How to Construct Parallel Lines(With Steps & Examples)

how to construct parallel lines

This post is also available in: हिन्दी (Hindi)

The lines that do not intersect each other and have the same distance between them from any point of the lines are called parallel lines. In other words, parallel lines are non-intersecting lines having a constant distance. The railway tracks are the best example of parallel lines.

Let’s understand how to construct parallel lines with steps and examples using ruler and compass and using a ruler and set square.

Properties of Parallel Lines

The following are the main properties of parallel lines.

  • The corresponding angles formed by parallel lines are equal.
  • The vertically opposite angles formed by parallel lines are equal.
  • The alternate interior angles formed by parallel lines are equal.
  • The alternate exterior angles formed by parallel lines are equal.
  • The pair of interior angles on the same side of the transversal are supplementary, that is they equal to $180^{\circ}$.

How to Construct Parallel Lines Through a Point Not Lying on a Given Line

You can use any one of the properties regarding the transversal and parallel lines to construct parallel lines using ruler and compasses only.

Steps to Construct Parallel Lines Through a Point Not Lying on a Given Line

The following steps are used to construct parallel lines through a point not lying on a given line.

Step 1: Take a line $l$ and a point $\text{A}$ outside $l$.

how to construct parallel lines

Step 2: Take any point $\text{B}$ on $l$ and join $\text{B}$ to $\text{A}$.

how to construct parallel lines

Step 3: With $\text{B}$ as centre and a convenient radius, draw an arc cutting $l$ at $\text{C}$ and $\text{BA}$ at $\text{D}$.

how to construct parallel lines

Step 4: Now with $\text{A}$ as centre and the same radius as in Step 3, draw an arc $\text{EF}$ cutting $\text{AB}$ at $\text{G}$.

how to construct parallel lines

Step 5: Place the pointed tip of the compass at $\text{C}$ and adjust the opening so that the pencil tip is at $\text{D}$.

Step 6: With the same opening as in Step 5 and with $\text{G}$ as centre, draw an arc cutting the arc $\text{EF}$ at $\text{H}$.

how to construct parallel lines

Step 7: Now, join $\text{AH}$ to draw a line $m$.

how to construct parallel lines

Line $m$ is parallel to the given line $l$.

how to construct parallel lines
Is your child struggling with Maths?
frustrated-kid
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
  • Réunion 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

Construction of Parallel Lines Using Set Square

You can also use a set square to construct parallel lines.

Steps for Construction of Parallel Lines Using Set Square

The following steps are used for the construction of parallel lines using set square.

Step 1: Position an edge of the set square against a ruler and draw a line along one of the other edges.

how to construct parallel lines

Step 2: Slide the set square into a new position while keeping the ruler fixed exactly at the same position.

how to construct parallel lines

Step 3: Draw a line along the same edge that was used in Step 1.

how to construct parallel lines

Line $l$ is parallel to line $m$, i.e, $l || m$

how to construct parallel lines
Famous Math Competitions for Kids

Practice Problems

  1. What are parallel lines?
  2. What are the properties of parallel lines?
  3. Which property of parallel lines is used to construct using a ruler and compass?
  4. Draw a line segment of 7.8 cm and then draw a line parallel to it.

FAQs

Can we construct parallel lines using a set square?

how to construct parallel lines

Yes, we can construct parallel lines using a set square. The steps involved are
Step 1: Position an edge of the set square against a ruler and draw a line along one of the other edges.
Step 2: Slide the set square into a new position while keeping the ruler fixed exactly at the same position.
Step 3: Draw a line along the same edge that was used in Step 1.

Which property of parallel lines is used to construct using a ruler and compass?

For constructing a line parallel to a given line we have to measure the inclination of the given angle with the reference and draw the same degree of inclination with the reference to get the line parallel to the given line.

Conclusion

The lines that do not intersect each other and have the same distance between them from any point of the lines are called parallel lines. The parallel lines can be constructed using a ruler and compass and also using a ruler and set square.

Recommended Reading

{"email":"Email address invalid","url":"Website address invalid","required":"Required field missing"}
>