{"id":6944,"date":"2014-04-15T17:03:13","date_gmt":"2014-04-15T17:03:13","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6944"},"modified":"2014-12-02T08:25:30","modified_gmt":"2014-12-02T08:25:30","slug":"math-review-of-angles-and-parallel-lines","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-angles-and-parallel-lines\/","title":{"rendered":"Math Review of Angles and Parallel Lines"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

Angles and the lines that form them are an essential part of geometry.\u00a0 Understanding the relationship between parallel lines, lines that are not parallel, and the different types of angles within figures is important to determining their measurement.<\/p>\n

What Are the Relationships Between Angles on a Straight Line?<\/strong><\/p>\n

Suppose that three points A, B, and C are all on the same line.\u00a0 Then \u2220ABC measures 180o<\/sup> by definition.\u00a0 If a ray goes between point B through point D, two new angles are formed, \u2220DBC and \u2220DBA.\u00a0 Those angles are called a linear pair because they have a common side, ray DB.\u00a0 The measurements of a linear pair, because the angles are on a straight line, add up to the same measurement as a straight line, or 180o<\/sup>.\u00a0 If \u2220DBC measures 70o<\/sup>, then \u2220DBA measures 180-70, or 110o<\/sup>.\u00a0 Similarly, if \u2220DBC measures 135o<\/sup>, then \u2220DBA measures 180-135, or 45\u00b0.<\/p>\n

What Are Vertical Angles?<\/strong><\/p>\n

Suppose that ray DB were extended through point B and point E into a line.\u00a0 There would then be two new angles, \u2220EBC and \u2220EBA.\u00a0 There are now two new linear pairs, \u2220DBA and \u2220EBA and \u2220DBC and \u2220EBC.\u00a0 Suppose that \u2220DBC measures 70\u00b0, then \u2220EBC measures 110\u00b0, or 180-70.\u00a0 Since \u2220DBC and \u2220DBA are a linear pair, \u2220DBA also measures 110\u00b0, the same as \u2220EBC.\u00a0 The angles \u2220DBA and \u2220EBA are also a linear pair, and since \u2220DBA measures 110\u00b0, \u2220EBA measures 180-110, or 70\u00b0, the same as \u2220DBC.\u00a0 The angles \u2220DBA and \u2220EBC are opposite each other, as are the angles \u2220DBC and \u2220EBA.\u00a0 They are called vertical angles, and vertical angles have the same measurement.<\/p>\n

What Are Parallel Lines?<\/strong><\/p>\n

Parallel lines are on the same plane, but do not have any points in common.\u00a0 They never meet at any point on the plane.\u00a0 Suppose a parallel line to the line containing points A, B, and C were drawn through point D.\u00a0 That line contained points F and G, as well as D, and none of those points are on line ABC. The line BDE that intersects both parallel lines is called a transversal.\u00a0 The only point it has in common with line ABC is point B, and the only point it has in common with line FDG is point D.<\/p>\n

What Is the Measurement of Angles Created by Parallel Lines?<\/strong><\/p>\n

Parallel lines go in the same direction, so the measurements of the new angles created by the intersection of the transversal with the new parallel line are equal to the measurements of the intersection of the transversal with the original line.\u00a0 Those angles are called corresponding angles.<\/p>\n

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Overview: Angles and the lines that form them are an essential part of geometry.\u00a0 Understanding the relationship between parallel lines, lines that are not parallel, and the different types of angles within figures is important to determining their measurement. What Are the Relationships Between Angles on a Straight Line? Suppose that three points A, B, […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[10,13],"tags":[96,1281,1849,2681],"class_list":["post-6944","post","type-post","status-publish","format-standard","hentry","category-geometry","category-pre-algebra","tag-angles","tag-parallel-lines","tag-transversal","tag-vertical-angles"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6944","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=6944"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6944\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6944"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6944"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6944"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}