{"id":156152,"date":"2022-03-26T01:26:24","date_gmt":"2022-03-25T19:56:24","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/parallelogram-definition-types-properties\/"},"modified":"2024-08-21T16:02:48","modified_gmt":"2024-08-21T10:32:48","slug":"parallelogram-definition-types-properties","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram\/","title":{"rendered":"Parallelogram"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram\/#Parallelogram_Definition\" title=\"Parallelogram Definition\">Parallelogram Definition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram\/#Shape_of_Parallelogram\" title=\"Shape of Parallelogram\">Shape of Parallelogram<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram\/#Angles_of_Parallelogram\" title=\"Angles of Parallelogram\">Angles of Parallelogram<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram\/#Area_of_Parallelogram\" title=\"Area of Parallelogram\">Area of Parallelogram<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram\/#Perimeter_of_Parallelogram\" title=\"Perimeter of Parallelogram\">Perimeter of Parallelogram<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram\/#Properties_of_Parallelogram\" title=\"Properties of Parallelogram\">Properties of Parallelogram<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram\/#Parallelogram_Theorems\" title=\"Parallelogram Theorems\">Parallelogram Theorems<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram\/#Difference_between_Parallelogram_and_Rhombus\" title=\"Difference between Parallelogram and Rhombus\">Difference between Parallelogram and Rhombus<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram\/#FAQs_on_Parallelogram\" title=\"FAQs on Parallelogram\">FAQs on Parallelogram<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram\/#Define_Parallelogram\" title=\"Define Parallelogram\">Define Parallelogram<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram\/#Give_some_examples_of_a_parallelogram\" title=\"Give some examples of a parallelogram.\">Give some examples of a parallelogram.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram\/#Write_some_of_the_properties_of_a_parallelogram\" title=\"Write some of the properties of a parallelogram.\">Write some of the properties of a parallelogram.<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>A <strong>parallelogram<\/strong> is a polygon that has a two-dimensional geometrical shape. A parallelogram has four sides. The sides of a parallelogram are parallel to each other. Parallel sides have equal lengths in a parallelogram. If we add the adjacent angles of a parallelogram, the sum is equal to 180\u2070.<\/p>\n<p>In this article, we will study about shape of parallelograms, angles of parallelograms, properties of parallelogram, area and perimeter of parallelograms, and parallelogram theorems.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Parallelogram_Definition\"><\/span>Parallelogram Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A parallelogram has two pairs of parallel lines. It is a quadrilateral in which opposite sides are equal in length. Opposite angles of a parallelogram are also equal when measured. The sum of all the interior angles of a parallelogram equals 360\u2070.<\/p>\n<p>In a parallelogram, interior angles of the same side of a transversal are supplementary.<\/p>\n<p>Below given is the figure of a parallelogram:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-730274\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Parallelogram.png\" alt=\"Parallelogram\" width=\"160\" height=\"91\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Parallelogram.png 160w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Parallelogram-150x85.png 150w\" sizes=\"(max-width: 160px) 100vw, 160px\" \/><\/p>\n<p>Here, ABCD is a parallelogram.<\/p>\n<p>AB || CD and AD || BC.<\/p>\n<p>AB = CD and AD = BC.<\/p>\n<p>And \u2220A = \u2220C and \u2220B = \u2220D.<\/p>\n<p>\u2220A and \u2220D are supplementary angles as these interior angles are lying on the same side of the transversal. Same, \u2220 B and \u2220C are supplementary angles.<\/p>\n<p>Therefore,<\/p>\n<p>\u2220A + \u2220D = 180<\/p>\n<p>\u2220 B + \u2220C = 180<\/p>\n<p style=\"text-align: center;\"><em><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/formulas\/parallelogram-formula\/\">Parallelogram Formula<\/a><\/strong><\/em><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Shape_of_Parallelogram\"><\/span>Shape of Parallelogram<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A parallelogram has a two dimensional shape. It has four sides in which two pairs of sides are parallel and equal. In case, if the length of the two sides are not equal, that shape will not be considered as a parallelogram. The opposite interior angles of a parallelogram should also be equal, of they are not equal, it will not be a parallelogram.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Angles_of_Parallelogram\"><\/span>Angles of Parallelogram<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A parallelogram is a two dimensional shape having four angles. In a parallelogram, opposite interior angles are equal. The angels which are present on the same sides of the transversal are supplementary. The sum of the interior angles of a parallelogram is 360\u2070.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Area_of_Parallelogram\"><\/span>Area of Parallelogram<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The region occupied by a parallelogram in a two-dimensional plane is the area of a parallelogram. Below discussed is the formula to find the area of a parallelogram:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-730275\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Area-of-Parallelogram.png\" alt=\"Area of Parallelogram\" width=\"245\" height=\"133\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Area-of-Parallelogram.png 245w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Area-of-Parallelogram-150x81.png 150w\" sizes=\"(max-width: 245px) 100vw, 245px\" \/><\/p>\n<p style=\"text-align: left;\"><strong>       Area = Base \u00d7 Height<\/strong><\/p>\n<p>In the above parallelogram, ABCD, the area is given by:<\/p>\n<p>Area = ab sin A = ba sin B<\/p>\n<p>Where a is the slant length of the side of a parallelogram and b is the base<\/p>\n<p style=\"text-align: center;\"><em><strong>Do Check: <a href=\"https:\/\/infinitylearn.com\/surge\/formulas\/diagonal-of-parallelogram-formula\/\">Diagonal of Parallelogram Formula<\/a><\/strong><\/em><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Perimeter_of_Parallelogram\"><\/span>Perimeter of Parallelogram<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The perimeter of a parallelogram can be calculated as the total length of the distance of the boundaries of the parallelogram. The values of length and breadth should be known to calculate the perimeter of the parallelogram. The opposite sides of a parallelogram when measured, are equal. The formula used to calculate the perimeter of a parallelogram is as follows:<\/p>\n<p><strong>Perimeter = 2 (a+b) units , <\/strong>where a and b are the lengths of the sides of a parallelogram.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Properties_of_Parallelogram\"><\/span>Properties of Parallelogram<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The properties of a parallelogram are written below:<\/p>\n<ul>\n<li>The opposite sides of a parallelogram are equal and parallel as well as the opposite angles are also equal.<\/li>\n<li>The adjacent angles are also equal.<\/li>\n<li>In a parallelogram, if any one angle is right angle, then all the other angles will also be right angle.<\/li>\n<li>The two diagonals of a parallelogram bisect each other.<\/li>\n<li>The two diagonals bisect the parallelogram into two congruent triangles.<\/li>\n<li>In a parallelogram, the sum of the square of all the sides is equal to the sum of the square of its diagonals.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Parallelogram_Theorems\"><\/span>Parallelogram Theorems<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Theorem 1: Parallelograms that are present on the same base and between the same parallel sides are equal in area.<\/strong><\/p>\n<p><strong>Proof:<\/strong> Two parallelograms ABCD and ABEF are on the same base DC and are between the same parallel lines AB and FC.<\/p>\n<p>To prove area of ABCD = area of ABEF.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-730276\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Parallelogram-Theorem-1.png\" alt=\"Parallelogram Theorem 1\" width=\"161\" height=\"95\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Parallelogram-Theorem-1.png 161w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Parallelogram-Theorem-1-150x89.png 150w\" sizes=\"(max-width: 161px) 100vw, 161px\" \/><\/p>\n<p>In \u2206ADF and \u2206BCE,<\/p>\n<p>AD = BC and AF = BE. ( ABCD and ABEF are parallelograms).<\/p>\n<p>\u2220ADF = \u2220BCE (corresponding angles)<\/p>\n<p>\u2220AFD = \u2220BEC (corresponding angles)<\/p>\n<p>\u2220DAF = \u2220CBE (corresponding angles)<\/p>\n<p>Therefore, \u2206ADE \u2248 \u2206BCF (SAS rule)<\/p>\n<p>Area \u2206 ADF = Area \u2206 BCE (By congruence area axiom)<\/p>\n<p>Area(ABCD) = Area(ABED) + Area(BCE)<\/p>\n<p>Area(ABCD) = Area(ABED)+Area(ADF)<\/p>\n<p>Area(ABCD) = Area(ABEF)<\/p>\n<p>Hence, Parallelograms that are present on the same base and between the same parallel sides are equal in area.<\/p>\n<p style=\"text-align: center;\"><em><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/articles\/area-of-parallelogram\/\">Area of Parallelogram<\/a><\/strong><\/em><\/p>\n<p><strong>Theorem 2: The area of a parallelogram is the result of the product of its base and the corresponding altitude.<\/strong><\/p>\n<p><strong>Given:<\/strong> AB is the base in a parallelogram ABCD.<\/p>\n<p><strong>To prove:<\/strong> Area of Parallelogram = AB \u00d7 AL<\/p>\n<p><strong>Construction:<\/strong> Draw a BM perpendicular to CD.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-730277\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Parallelogram-Theorem-2.png\" alt=\"Parallelogram Theorem 2\" width=\"154\" height=\"93\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Parallelogram-Theorem-2.png 154w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Parallelogram-Theorem-2-150x91.png 150w\" sizes=\"(max-width: 154px) 100vw, 154px\" \/><\/p>\n<p>In the given figure, the base of the rectangle ABCD and rectangle ABML are the same. They are also between the same parallel lines AB and LC.<\/p>\n<p>Area of Parallelogram ABCD = Area of Parallelogram ABML.<\/p>\n<p>Area of rectangle = length \u00d7 breadth<\/p>\n<p>Area of Parallelogram ABCD = AB \u00d7 AL<\/p>\n<p>Therefore, the area of a parallelogram is the result of the product of its base and the corresponding altitude.<\/p>\n<p style=\"text-align: center;\"><em><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/formulas\/perimeter-of-a-parallelogram-formula\/\">Perimeter of a Parallelogram Formula<\/a><\/strong><\/em><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Difference_between_Parallelogram_and_Rhombus\"><\/span>Difference between Parallelogram and Rhombus<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"table-responsive\">\n<table class=\"table table-bordered table-striped\" style=\"width: 74.0508%; height: 115px;\" cellspacing=\"0\" cellpadding=\"5\">\n<tbody>\n<tr style=\"background-color: #89cff0; color: black;\">\n<td style=\"text-align: center;\"><b>Parallelogram <\/b><\/td>\n<td style=\"text-align: center;\"><b>Rhombus <\/b><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">A parallelogram is a quadrilateral. It\u2019s opposite sides are both equal and parallel. <\/span><\/td>\n<td><span style=\"font-weight: 400;\">A rhombus is a quadrilateral. All the sides are congruent in it. <\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">The diagonals of a parallelogram bisect each other.<\/span><\/td>\n<td><span style=\"font-weight: 400;\">The diagonals of a rhombus bisect each other at a right angle.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">In a parallelogram, opposite angles are equal. <\/span><\/td>\n<td><span style=\"font-weight: 400;\">In a rhombus, opposite angles are equal. <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2><span class=\"ez-toc-section\" id=\"FAQs_on_Parallelogram\"><\/span>FAQs on Parallelogram<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Define_Parallelogram\"><\/span>Define Parallelogram<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tA parallelogram is a polygon which has a two dimensional geometrical shape. The sides of a parallelogram are parallel to each other. A parallelogram has four sides. Parallel sides have equal length in a parallelogram. If we add the adjacent angles of a parallelogram, the sum is equal to 180\u2070.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Give_some_examples_of_a_parallelogram\"><\/span>Give some examples of a parallelogram.<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tA parallelogram has two pairs of parallel lines. It is a quadrilateral in which opposite sides are equal in length. In a parallelogram, opposite angles are equal. The sum of all the interior angles of a parallelogram equals 360\u2070\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Write_some_of_the_properties_of_a_parallelogram\"><\/span>Write some of the properties of a parallelogram.<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tSome of the properties of a parallelogram are: The opposite sides of a parallelogram are equal and parallel as well as the opposite angles are also equal. The adjacent angles are equal. In a parallelogram, if any one angle is right angle, then all the other angles will also be right angle. The two diagonals of a parallelogram bisect each other. The two diagonals bisect the parallelogram into two congruent triangles\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Define Parallelogram\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"A parallelogram is a polygon which has a two dimensional geometrical shape. The sides of a parallelogram are parallel to each other. A parallelogram has four sides. Parallel sides have equal length in a parallelogram. If we add the adjacent angles of a parallelogram, the sum is equal to 180\u2070.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Give some examples of a parallelogram.\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"A parallelogram has two pairs of parallel lines. It is a quadrilateral in which opposite sides are equal in length. In a parallelogram, opposite angles are equal. The sum of all the interior angles of a parallelogram equals 360\u2070\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Write some of the properties of a parallelogram.\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Some of the properties of a parallelogram are: The opposite sides of a parallelogram are equal and parallel as well as the opposite angles are also equal. The adjacent angles are equal. In a parallelogram, if any one angle is right angle, then all the other angles will also be right angle. The two diagonals of a parallelogram bisect each other. The two diagonals bisect the parallelogram into two congruent triangles\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>A parallelogram is a polygon that has a two-dimensional geometrical shape. A parallelogram has four sides. The sides of a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Parallelogram","_yoast_wpseo_title":"Understanding Parallelogram: Properties, Formulas, and Examples | Infinity Learn","_yoast_wpseo_metadesc":"Explore the properties, formulas, and examples of a parallelogram. 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