{"id":4007,"date":"2012-09-28T14:10:35","date_gmt":"2012-09-28T14:10:35","guid":{"rendered":"http:\/\/schooltutoring.com\/scholarship\/?p=4007"},"modified":"2014-12-02T08:32:01","modified_gmt":"2014-12-02T08:32:01","slug":"geometry-relations-of-lines","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/09\/28\/geometry-relations-of-lines\/","title":{"rendered":"Geometry: Relations of Lines"},"content":{"rendered":"<p>In Geometry, lines can relate in a variety of ways, such as intersecting, and transverse.<\/p>\n<h5>Intersecting lines:<\/h5>\n<p>Two or more lines which are passing through a common point are called intersecting lines.<\/p>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/09\/pair-of-lines1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4008\" title=\"pair of lines1\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/09\/pair-of-lines1.jpg\" alt=\"\" width=\"143\" height=\"108\" \/><\/a><\/p>\n<h5>Transverse:<\/h5>\n<p>Many times we might have observed that some railway lines crossing many other lines. This gives the concept of transversal.<\/p>\n<p>A <strong><em>transversal<\/em><\/strong> is a line which intersects two or more points at different points.<\/p>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/09\/pair-of-lines2.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4009\" title=\"pair of lines2\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/09\/pair-of-lines2.jpg\" alt=\"\" width=\"125\" height=\"87\" \/><\/a><\/p>\n<h5>Angles made by a transversal:<\/h5>\n<p>If a transversal <strong><em>l<\/em><\/strong> cuts two lines <strong><em>a<\/em><\/strong> and <strong><em>b<\/em><\/strong> then 8 angles are formed at the intersection points. We have some particular names for the angles thus formed.<\/p>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/09\/pair-of-lines3.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4010\" title=\"pair of lines3\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/09\/pair-of-lines3.jpg\" alt=\"\" width=\"200\" height=\"159\" \/><\/a><\/p>\n<p>a)\u00a0\u00a0\u00a0\u00a0\u00a0 Interior angles:<\/p>\n<p>The angles which are formed inside the lines a and b are called interior angles. Here, \u22203, \u22204, \u22205 and \u22206 are the interior angles.<\/p>\n<p>b)\u00a0\u00a0\u00a0 Exterior angles:<\/p>\n<p>The angles which are formed above the line a and below the line b are called the exterior angles. Here, \u22201, \u22202, \u22208 and \u22207 are the exterior angles.<\/p>\n<p>c)\u00a0\u00a0\u00a0\u00a0 Corresponding angles:<\/p>\n<p>The angles which lie on the same relative position are called the corresponding angles.<\/p>\n<p>Here, 1 &amp;5, 2&amp;6, 4&amp;8 and 3&amp;7 are the pairs of corresponding angles.<\/p>\n<p>d)\u00a0\u00a0\u00a0 Alternate interior angles:<\/p>\n<p>Interior angles which are on the opposite side of the transversal are called alternate interior angles. Here, \u22204&amp;\u22206 and \u22203&amp;\u22205 are the alternate interior angles.<\/p>\n<p>e)\u00a0\u00a0\u00a0\u00a0 Alternate exterior angles:<\/p>\n<p>Exterior angles which are on the opposite side of the transversal are called alternate exterior angles. Here, \u22201&amp;\u22207 and \u22202&amp;\u22208 are the alternate exterior angles.<\/p>\n<h5>Transversal of parallel lines:<\/h5>\n<p>A transversal is a line cutting any two lines. But if a transversal cuts two parallel lines there are some pairs of angles which are equal and are stated as follows.<\/p>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/09\/pair-of-lines4.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-4011\" title=\"pair of lines4\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/09\/pair-of-lines4.jpg\" alt=\"\" width=\"152\" height=\"159\" \/><\/a><\/p>\n<p>Here, the transversal is cutting two parallel lines and in this case,<\/p>\n<p>a)\u00a0\u00a0\u00a0\u00a0 Pairs of alternate interior angles measure same.<\/p>\n<p>\u2220c = \u2220f and \u2220d = \u2220e.<\/p>\n<p>b)\u00a0\u00a0\u00a0 Pairs of exterior angles are same.<\/p>\n<p>\u2220a = \u2220h and \u2220b = \u2220g.<\/p>\n<p>c)\u00a0\u00a0\u00a0\u00a0 Pairs of corresponding angles are same.<\/p>\n<p>\u2220a = \u2220e , \u2220b = \u2220f, \u2220c = \u2220g and \u2220d= \u2220h.<\/p>\n<p>d)\u00a0\u00a0\u00a0 Each pair of interior angles on the same side of the transversal are supplementary.<\/p>\n<p>\u2220c+\u2220d = 180<sup>0<\/sup> and \u2220g+\u2220h = 180<sup>0<\/sup>.<\/p>\n<p>Do you also need help with your Writing? Take a look at our <a href=\"https:\/\/schooltutoring.com\/english-tutors\/\">Writing tutoring services.<\/a> <\/p>\n<p><span class=\"tutorOrange\">SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Fredericton visit: <a href=\"https:\/\/schooltutoring.com\/tutoring-in-fredericton-new-brunswick\/\">Tutoring in Fredericton.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In Geometry, lines can relate in a variety of ways, such as intersecting, and transverse. Intersecting lines: Two or more lines which are passing through a common point are called intersecting lines. Transverse: Many times we might have observed that some railway lines crossing many other lines. This gives the concept of transversal. A transversal [&hellip;]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[10],"tags":[410,558,953,1048,1274,1280,1849],"class_list":["post-4007","post","type-post","status-publish","format-standard","hentry","category-geometry","tag-corresponding","tag-ecterior","tag-interior","tag-lines","tag-pair","tag-parallel","tag-transversal"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/4007","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=4007"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/4007\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=4007"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=4007"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=4007"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}