{"id":271,"date":"2019-06-26T23:18:12","date_gmt":"2019-06-26T23:18:12","guid":{"rendered":"http:\/\/funfacts.104.42.120.246.xip.io\/?page_id=271"},"modified":"2019-12-09T21:20:58","modified_gmt":"2019-12-09T21:20:58","slug":"morleys-theorem","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/funfacts\/morleys-theorem\/","title":{"rendered":"Morley&#8217;s Theorem"},"content":{"rendered":"\n<div class=\"wp-block-image\"><figure class=\"alignright\"><img loading=\"lazy\" decoding=\"async\" width=\"322\" height=\"188\" data-attachment-id=\"1532\" data-permalink=\"https:\/\/math.hmc.edu\/funfacts\/morleys-theorem\/10005-2-1\/\" data-orig-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/12\/10005.2.1.gif\" data-orig-size=\"322,188\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"10005.2.1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/12\/10005.2.1.gif\" src=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/12\/10005.2.1.gif\" alt=\"\" class=\"wp-image-1532\"\/><\/figure><\/div>\n\n\n\n<p>Take any triangle. Mark the 3 points which are the intersections of adjacent angle trisectors. No matter what triangle you start with, these 3 points will form an equilateral triangle!<\/p>\n\n\n\n<p><strong>Presentation&nbsp;Suggestions:<\/strong><br>Draw a picture and invite students to draw their own triangle on a sheet of paper and follow along.<\/p>\n\n\n\n<p><strong>The\u00a0Math\u00a0Behind\u00a0the\u00a0Fact:<\/strong><br>This is yet another surprising fact from\u00a0geometry. Can you think of a proof?<\/p>\n\n\n\n<p><strong>How to Cite this Page:<\/strong><br>Su, Francis E., et al. &#8220;Morley&#8217;s Theorem.&#8221;&nbsp;<em>Math Fun Facts<\/em>. &lt;http:\/\/www.math.hmc.edu\/funfacts&gt;.\n\n<\/p>\n\n\n\n<p><strong>Fun Fact suggested by:   <\/strong><br>Jorge Aarao<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Take any triangle. Mark the 3 points which are the intersections of adjacent angle trisectors. No matter what triangle you&#46;&#46;&#46;<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[3,8],"class_list":["post-271","page","type-page","status-publish","hentry","tag-easy","tag-geometry"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/271","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/comments?post=271"}],"version-history":[{"count":3,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/271\/revisions"}],"predecessor-version":[{"id":1533,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/271\/revisions\/1533"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=271"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=271"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}