{"id":3485,"date":"2024-03-23T12:09:07","date_gmt":"2024-03-23T16:09:07","guid":{"rendered":"https:\/\/josmfs.net\/?p=3485"},"modified":"2024-03-23T12:09:07","modified_gmt":"2024-03-23T16:09:07","slug":"pythagorean-theorem-converse","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2024\/03\/23\/pythagorean-theorem-converse\/","title":{"rendered":"Pythagorean Theorem Converse"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-3483\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/03\/Pythagorean-Theorem-Converse-Fig2.jpg\" alt=\"\" width=\"200\" height=\"137\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/03\/Pythagorean-Theorem-Converse-Fig2.jpg 444w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/03\/Pythagorean-Theorem-Converse-Fig2-300x205.jpg 300w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>One of the joys of getting old is that you forget things.\u00a0\u00a0 So one of the things I recall is that the converse of the Pythagorean Theorem is true, that is, if a triangle with short sides <em>a<\/em> and <em>b<\/em> and long side <em>c<\/em> is such that<\/p>\n<p style=\"text-align: center;\"><em>a<\/em><sup>2<\/sup> + <em>b<\/em><sup>2<\/sup> = <em>c<\/em><sup>2<\/sup>,<\/p>\n<p>then the triangle must be a right triangle with the angle between sides <em>a<\/em> and <em>b<\/em> being 90\u00b0.\u00a0 But I didn\u2019t recall how to prove it.\u00a0 So I thought I would see if I could do it without looking up any sources.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/03\/Pythagorean-Theorem-Converse-240320.pdf\">Pythagorean Theorem Converse<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>One of the joys of getting old is that you forget things.\u00a0\u00a0 So one of the things I recall is that the converse of the Pythagorean Theorem is true, that is, if a triangle with short sides a and b and long side c is such that a2 + b2 = c2, then the triangle [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[30],"class_list":["post-3485","post","type-post","status-publish","format-standard","hentry","category-curiosities-and-questions","tag-pythagorean-theorem"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3485","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=3485"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3485\/revisions"}],"predecessor-version":[{"id":3487,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3485\/revisions\/3487"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=3485"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=3485"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=3485"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}