{"id":2311,"date":"2021-07-31T12:43:31","date_gmt":"2021-07-31T16:43:31","guid":{"rendered":"https:\/\/josmfs.net\/?p=2311"},"modified":"2021-07-31T12:43:31","modified_gmt":"2021-07-31T16:43:31","slug":"triangle-quadrangle-puzzle","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2021\/07\/31\/triangle-quadrangle-puzzle\/","title":{"rendered":"Triangle Quadrangle Puzzle"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2309\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/07\/Triangle-Quadrangle-Fig2.jpg\" alt=\"\" width=\"200\" height=\"136\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/07\/Triangle-Quadrangle-Fig2.jpg 378w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/07\/Triangle-Quadrangle-Fig2-300x204.jpg 300w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>This is another simple problem from <em>Five Hundred Mathematical Challenges<\/em>:<\/p>\n<p><strong>\u201cProblem 57.<\/strong>\u00a0 Let <em>X<\/em> be any point between <em>B<\/em> and <em>C<\/em> on the side <em>BC<\/em> of the convex quadrilateral <em>ABCD <\/em>(as in the Figure).\u00a0 A line is drawn through <em>B <\/em>parallel to <em>AX <\/em>and another line is drawn through <em>C <\/em>parallel to <em>DX<\/em>.\u00a0 These two lines intersect at <em>P<\/em>.\u00a0 Prove that the area of the triangle <em>APD <\/em>is equal to the area of the quadrilateral <em>ABCD<\/em>.\u201d<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/07\/Triangle-Quadrangle-Puzzle-210222.pdf\">Triangle Quadrangle Puzzle<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is another simple problem from Five Hundred Mathematical Challenges: \u201cProblem 57.\u00a0 Let X be any point between B and C on the side BC of the convex quadrilateral ABCD (as in the Figure).\u00a0 A line is drawn through B parallel to AX and another line is drawn through C parallel to DX.\u00a0 These two [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[177,13],"class_list":["post-2311","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-500-math-challenges","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2311","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=2311"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2311\/revisions"}],"predecessor-version":[{"id":2312,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2311\/revisions\/2312"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2311"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2311"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2311"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}