{"id":7697,"date":"2022-09-16T07:34:20","date_gmt":"2022-09-16T07:34:20","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=7697"},"modified":"2022-09-16T07:34:20","modified_gmt":"2022-09-16T07:34:20","slug":"derivation-of-pythagorean-theorem-formula","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/09\/16\/derivation-of-pythagorean-theorem-formula\/","title":{"rendered":"Derivation of Pythagorean Theorem Formula"},"content":{"rendered":"\n<p>Consider a right-angled triangle ABC, right-angled at B. Draw a perpendicular BD meeting AC at D.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/mdr.foobrdigital.com\/wp-content\/uploads\/2022\/09\/dsdsdssds-1-1024x585.png\" alt=\"\" class=\"wp-image-7699\"\/><\/figure>\n\n\n\n<p>In \u25b3ABD and \u25b3ACB,<\/p>\n\n\n\n<ul><li>\u2220A = \u2220A (common)<\/li><li>\u2220ADB = \u2220ABC (both are right angles)<\/li><\/ul>\n\n\n\n<p>Thus, \u25b3ABD \u223c \u25b3ACB (by AA similarity criterion)<\/p>\n\n\n\n<p>Similarly, we can prove \u25b3BCD \u223c \u25b3ACB.<\/p>\n\n\n\n<p>Thus \u25b3ABD \u223c \u25b3ACB, Therefore, AD\/AB = AB\/AC. We can say that AD \u00d7 AC = AB<sup>2<\/sup>.<\/p>\n\n\n\n<p>Similarly, \u25b3BCD \u223c \u25b3ACB. Therefore,CD\/BC = BC\/AC. We can also say that CD \u00d7 AC = BC<sup>2<\/sup>.<\/p>\n\n\n\n<p>Adding these 2 equations, we get AB<sup>2<\/sup>&nbsp;+ BC<sup>2&nbsp;<\/sup>= (AD \u00d7 AC) + (CD \u00d7 AC)<\/p>\n\n\n\n<p>AB<sup>2<\/sup>&nbsp;+ BC<sup>2&nbsp;<\/sup>=AC(AD +DC)<\/p>\n\n\n\n<p>AB<sup>2<\/sup>&nbsp;+ BC<sup>2&nbsp;<\/sup>=AC<sup>2<\/sup><\/p>\n\n\n\n<p>Hence proved.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Pythagoras Theorem Triangles<\/h2>\n\n\n\n<p>Right triangles follow the rule of the Pythagoras theorem and they are called Pythagoras theorem triangles. The three sides of such a triangle are collectively called\u00a0Pythagoras triples. All the Pythagoras theorem triangles follow the Pythagoras theorem which says that the square of the hypotenuse is equal to the sum of the two sides of the right-angled triangle. This can be expressed as c<sup>2<\/sup>\u00a0= a<sup>2<\/sup>\u00a0+ b<sup>2<\/sup>; where &#8216;c&#8217; is the hypotenuse and &#8216;a&#8217; and &#8216;b&#8217; are the two legs of the triangle.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Pythagoras Theorem Squares<\/h2>\n\n\n\n<p>As per the Pythagorean theorem, the area of the square which is built upon the hypotenuse of a right triangle is equal to the sum of the area of the squares built upon the other two sides. These squares are known as Pythagoras squares.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Consider a right-angled triangle ABC, right-angled at B. Draw a perpendicular BD meeting AC at D. In \u25b3ABD and \u25b3ACB, \u2220A = \u2220A (common) \u2220ADB = \u2220ABC (both are right angles) Thus, \u25b3ABD \u223c \u25b3ACB (by AA similarity criterion) Similarly, we can prove \u25b3BCD \u223c \u25b3ACB. Thus \u25b3ABD \u223c \u25b3ACB, Therefore, AD\/AB = AB\/AC. We [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[304],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7697"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=7697"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7697\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=7697"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=7697"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=7697"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}