{"id":2598,"date":"2022-02-26T15:31:25","date_gmt":"2022-02-26T20:31:25","guid":{"rendered":"https:\/\/josmfs.net\/?p=2598"},"modified":"2022-02-26T15:31:25","modified_gmt":"2022-02-26T20:31:25","slug":"playing-with-triangles","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2022\/02\/26\/playing-with-triangles\/","title":{"rendered":"Playing with Triangles"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2596\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/02\/Playing-with-Triangles-Fig2.jpg\" alt=\"\" width=\"201\" height=\"199\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/02\/Playing-with-Triangles-Fig2.jpg 402w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/02\/Playing-with-Triangles-Fig2-300x297.jpg 300w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/02\/Playing-with-Triangles-Fig2-150x150.jpg 150w\" sizes=\"auto, (max-width: 201px) 100vw, 201px\" \/>Here is another elegant <em>Quantum<\/em> math magazine Brainteaser from the imaginative V. Proizvolov.<\/p>\n<p>\u201cTwo isosceles right triangles are placed one on the other so that the vertices of each of their right angles lie on the hypotenuse of the other triangle (see the figure at left). Their other four vertices form a quadrilateral. Prove that its area is divided in half by the segment joining the right angles. (V. Proizvolov)\u201d<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/02\/Playing-with-Triangles-200727.pdf\">Playing with Triangles<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is another elegant Quantum math magazine Brainteaser from the imaginative V. Proizvolov. \u201cTwo isosceles right triangles are placed one on the other so that the vertices of each of their right angles lie on the hypotenuse of the other triangle (see the figure at left). Their other four vertices form a quadrilateral. Prove that [&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":[13,194],"class_list":["post-2598","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-plane-geometry","tag-quantum-magazine"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2598","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=2598"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2598\/revisions"}],"predecessor-version":[{"id":2599,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2598\/revisions\/2599"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2598"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2598"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2598"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}