{"id":9023,"date":"2020-12-04T07:02:41","date_gmt":"2020-12-04T01:32:41","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=9023"},"modified":"2020-12-04T15:03:19","modified_gmt":"2020-12-04T09:33:19","slug":"angles-parallel-lines","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/angles-parallel-lines\/","title":{"rendered":"Angles with Parallel Lines"},"content":{"rendered":"<h2><span style=\"color: #00ccff;\">Angles with Parallel Lines<\/span><\/h2>\n<p>A<strong> transversal<\/strong> is a line that intersects two or more lines (in the same plane). When lines intersect, angles are formed in several locations. Certain angles are given &#8220;names&#8221; that describe &#8220;where&#8221; the angles are located in relation to the lines. These names describe angles whether the lines involved are parallel or not parallel.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-123965 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-1.png\" alt=\"Angles with Parallel Lines 1\" width=\"361\" height=\"192\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-1.png 361w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-1-300x160.png 300w\" sizes=\"(max-width: 361px) 100vw, 361px\" \/><\/p>\n<p><strong>Remember that:<\/strong><br \/>\nthe word <strong>INTERIOR<\/strong> means <strong>BETWEEN<\/strong> the lines.<br \/>\nthe word <strong>EXTERIOR<\/strong> means <strong>OUTSIDE<\/strong> the lines.<br \/>\nthe word <strong>ALTERNATE<\/strong> means &#8220;<strong>alternating sides<\/strong>&#8221; of the transversal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-123967\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-2.jpg\" alt=\"Angles with Parallel Lines 2\" width=\"698\" height=\"269\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-2.jpg 698w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-2-300x116.jpg 300w\" sizes=\"(max-width: 698px) 100vw, 698px\" \/><\/p>\n<p><iframe loading=\"lazy\" title=\"Angles in parallel lines (Edexcel GCSE Maths)\" width=\"1200\" height=\"900\" src=\"https:\/\/www.youtube.com\/embed\/PPQANycmBno?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/p>\n<p>The names &#8220;alternate interior angles&#8221;, &#8220;alternate exterior angles&#8221;, &#8220;corresponding angles&#8221;, and &#8220;interior angles on the same side of the transversal&#8221; are used to describe specific angles formed when lines intersect. These names are used both when lines are parallel and when lines are not parallel.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-123968 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-3.png\" alt=\"Angles with Parallel Lines 3\" width=\"441\" height=\"524\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-3.png 441w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-3-252x300.png 252w\" sizes=\"(max-width: 441px) 100vw, 441px\" \/><\/p>\n<p>Let&#8217;s examine these angles, and other angles, when the lines are parallel.<\/p>\n<p><strong>When the lines are parallel:<\/strong><\/p>\n<h3><span style=\"color: #0000ff;\">Alternate Interior Angles (measures are equal)<\/span><\/h3>\n<p>The name clearly describes &#8220;where&#8221; these angles are located.<br \/>\nLook carefully at the diagram below:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-123970\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-4.jpg\" alt=\"Angles with Parallel Lines 4\" width=\"455\" height=\"242\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-4.jpg 455w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-4-300x160.jpg 300w\" sizes=\"(max-width: 455px) 100vw, 455px\" \/><br \/>\nHint: If you draw a Z on the diagram, the alternate interior angles are found in the corners of the Z. The Z may also be a backward Z.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-123971\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-5.jpg\" alt=\"Angles with Parallel Lines 5\" width=\"336\" height=\"74\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-5.jpg 336w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-5-300x66.jpg 300w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><\/p>\n<p><strong>Theorem:<\/strong><br \/>\nIf two parallel lines are cut by a transversal, the alternate interior angles are congruent.<br \/>\n<strong>Theorem:<\/strong><br \/>\nIf two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel.<\/p>\n<p><strong>When the lines are parallel:<\/strong><\/p>\n<h3><span style=\"color: #0000ff;\">Alternate Exterior Angles (measures are equal)<\/span><\/h3>\n<p>The name clearly describes &#8220;where&#8221; these angles are located.<br \/>\nLook carefully at the diagram below:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-123972\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-6.jpg\" alt=\"Angles with Parallel Lines 6\" width=\"454\" height=\"244\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-6.jpg 454w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-6-300x161.jpg 300w\" sizes=\"(max-width: 454px) 100vw, 454px\" \/><\/p>\n<p><strong>Theorem:<\/strong><br \/>\nIf two parallel lines are cut by a transversal, the alternate exterior angles are congruent.<br \/>\n<strong>Theorem:<\/strong><br \/>\nIf two lines are cut by a transversal and the alternate exterior angles are congruent, the lines are parallel.<\/p>\n<p><strong>When the lines are parallel:<\/strong><\/p>\n<h3><span style=\"color: #0000ff;\">Corresponding Angles (measures are equal)<\/span><\/h3>\n<p>Unfortunately, the name of these angles does not clearly indicate &#8220;where&#8221; they are located. They are located:<\/p>\n<ul>\n<li>on the SAME SIDE of the transversal<\/li>\n<li>one INTERIOR and one EXTERIOR<\/li>\n<li>and they are NOT adjacent (they don&#8217;t touch).<br \/>\n(They lie on the same side of the transversal, in corresponding positions.)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-123973\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-7.jpg\" alt=\"Angles with Parallel Lines 7\" width=\"471\" height=\"242\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-7.jpg 471w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-7-300x154.jpg 300w\" sizes=\"(max-width: 471px) 100vw, 471px\" \/><br \/>\n<strong>Hint:<\/strong> If you took a picture of one corresponding angle and slid the angle up (or down) the same side of the transversal, you would arrive at the other corresponding angle.<br \/>\n<strong>Also:<\/strong> If you draw an F on the diagram, the corresponding angles can be found in the &#8220;corners&#8221; of the F. The F may be backward and\/or upside-down.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-123975\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-8.jpg\" alt=\"Angles with Parallel Lines 8\" width=\"323\" height=\"75\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-8.jpg 323w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-8-300x70.jpg 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><\/p>\n<p><strong>Theorem:<\/strong><br \/>\nIf two parallel lines are cut by a transversal, the corresponding angles are congruent.<br \/>\n<strong>Theorem:<\/strong><br \/>\nIf two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.<\/p>\n<p><strong>When the lines are parallel: <\/strong><\/p>\n<h3><span style=\"color: #0000ff;\">Interior Angles on the Same Side of the Transversal (measures are supplementary)<\/span><\/h3>\n<p>Their &#8220;name&#8221; is simply a description of where the angles are located.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-123976\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-9.jpg\" alt=\"Angles with Parallel Lines 9\" width=\"459\" height=\"241\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-9.jpg 459w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-9-300x158.jpg 300w\" sizes=\"(max-width: 459px) 100vw, 459px\" \/><\/p>\n<p><strong>Theorem:<\/strong><br \/>\nIf two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary.<br \/>\n<strong>Theorem:<\/strong><br \/>\nIf two lines are cut by a transversal and the interior angles on the same side of the transversal are supplementary, the lines are parallel.<\/p>\n<p>Of course, there are also other angle relationships occurring when working with parallel lines.<\/p>\n<h3><span style=\"color: #0000ff;\">Vertical Angles (measures are equal)<\/span><\/h3>\n<p>Vertical angles are ALWAYS equal, whether you have parallel lines or not.<br \/>\nRefresh your memory using the diagram below:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-123977\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-10.jpg\" alt=\"Angles with Parallel Lines 10\" width=\"370\" height=\"225\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-10.jpg 370w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-10-300x182.jpg 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><\/p>\n<p><strong>Theorem:<\/strong><br \/>\nVertical angles are congruent.<\/p>\n<h3><span style=\"color: #0000ff;\">Angles forming a Linear Pair: <\/span><\/h3>\n<p>(Adjacent Angles creating a Straight Line) (measures are supplementary)<br \/>\nThis is an &#8220;old&#8221; idea about angles revisited. Since a straight angle contains 180\u00b0, these two adjacent angles add to 180. They form a linear pair. (Adjacent angles share a vertex, share a side, and do not overlap.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-123978\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-11.jpg\" alt=\"Angles with Parallel Lines 11\" width=\"367\" height=\"221\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-11.jpg 367w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/04\/Angles-with-Parallel-Lines-11-300x181.jpg 300w\" sizes=\"(max-width: 367px) 100vw, 367px\" \/><\/p>\n<p><strong>Theorem:<\/strong><br \/>\nIf two angles form a linear pair, they are supplementary.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Angles with Parallel Lines A transversal is a line that intersects two or more lines (in the same plane). When lines intersect, angles are formed in several locations. Certain angles are given &#8220;names&#8221; that describe &#8220;where&#8221; the angles are located in relation to the lines. These names describe angles whether the lines involved are parallel &#8230; <a title=\"Angles with Parallel Lines\" class=\"read-more\" href=\"https:\/\/cbselibrary.com\/angles-parallel-lines\/\" aria-label=\"More on Angles with Parallel Lines\">Read more<\/a><\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[3295],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v18.4.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Angles with Parallel Lines - CBSE Library<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cbselibrary.com\/angles-parallel-lines\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Angles with Parallel Lines\" \/>\n<meta property=\"og:description\" content=\"Angles with Parallel Lines A transversal is a line that intersects two or more lines (in the same plane). 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When lines intersect, angles are formed in several locations. Certain angles are given &#8220;names&#8221; that describe &#8220;where&#8221; the angles are located in relation to the lines. These names describe angles whether the lines involved are parallel ... 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