{"id":5955,"date":"2013-05-21T04:42:07","date_gmt":"2013-05-21T04:42:07","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=5955"},"modified":"2014-12-02T08:27:01","modified_gmt":"2014-12-02T08:27:01","slug":"parallel-and-perpendicular-lines","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2013\/05\/21\/parallel-and-perpendicular-lines\/","title":{"rendered":"Parallel and Perpendicular Lines"},"content":{"rendered":"

Overview:\u00a0 Lines and Angles<\/strong>
\nLines in geometry exist in relationships to one another by the angles they form when they intersect.\u00a0 Those lines that do not intersect at all are parallel to each other.\u00a0 Those that intersect at one point or another form angles where they intersect.\u00a0 Perpendicular lines intersect at right angles, and have special relationships to one another.<\/p>\n

What Are Parallel Lines?<\/strong>
\nParallel lines do not intersect at any point.\u00a0 If they are in the same plane, parallel lines have the same tilt.\u00a0 When they are graphed, both lines have the same slope.\u00a0 If a transversal line crosses both parallel lines, the corresponding angles have the same measurement.\u00a0 This property of parallel lines allows students to deduce the measurement of one angle formed by one of the parallel lines and the transversal, if the measure of a corresponding angle is known.<\/p>\n

Parallel Lines Postulate<\/strong>
\nAs an example, in the figure below, lines a and b are parallel, and line t is a transversal cutting them.\u00a0 Suppose angle \u03b2 measures 1100<\/sup> where the transverse line t cuts through line a.\u00a0 Its corresponding angle where the transverse line t cuts through line b will also measure 1100<\/sup>.\u00a0 The measure of angle \u03b2 and angle \u03b8 is 1800<\/sup>, so angle \u03b8 (theta) measures 180-110 or 700<\/sup>.<\/p>\n

https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/8\/2013\/05\/Parallel_lines.png<\/a><\/p>\n

What \u00a0Are Perpendicular Lines?<\/strong>
\nPerpendicular lines exist in a special relationship to one another, as they intersect at a 900<\/sup> angle.\u00a0 They do not have to be horizontal or vertical, but just intersect at right angles.\u00a0 By extension of the Parallel Lines Theorem, if two lines are perpendicular to the same line, they are parallel to each other.\u00a0 If one angle measures 900<\/sup>, all the other angles (adjacent, vertical, and corresponding) that are formed by a transverse line cutting another line will also measure 900<\/sup>.\u00a0 Suppose angle \u03b2 in the figure above measures 900<\/sup>.\u00a0 Angle \u03b8 also measures 900<\/sup>.\u00a0 This application is also called the Perpendicular to Parallels Theorem.<\/p>\n

Construction of Parallel and Perpendicular Lines<\/strong>
\nGeometric properties of normal two-dimensional space ensure that parallel and perpendicular lines are readily constructed using nothing but an unmarked straightedge and compass.\u00a0 By using the endpoints of a line segment, students can construct another line perpendicular to that segment, and then construct a parallel line with the same slope as the first line. Students can use the process to demonstrate how the theorems work, by creating the transverse perpendicular to the first line, then constructing another line parallel to it.<\/p>\n

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Overview:\u00a0 Lines and Angles Lines in geometry exist in relationships to one another by the angles they form when they intersect.\u00a0 Those lines that do not intersect at all are parallel to each other.\u00a0 Those that intersect at one point or another form angles where they intersect.\u00a0 Perpendicular lines intersect at right angles, and have […]<\/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],"tags":[730,1281,1320],"class_list":["post-5955","post","type-post","status-publish","format-standard","hentry","category-geometry","tag-geometric-constructions","tag-parallel-lines","tag-perpendicular-lines"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5955","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\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=5955"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5955\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=5955"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=5955"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=5955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}