{"id":6295,"date":"2013-08-19T02:14:22","date_gmt":"2013-08-19T02:14:22","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6295"},"modified":"2014-12-02T08:26:58","modified_gmt":"2014-12-02T08:26:58","slug":"review-of-the-pythagorean-theorem","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/review-of-the-pythagorean-theorem\/","title":{"rendered":"Review of the Pythagorean Theorem"},"content":{"rendered":"<p><strong>Overview:<\/strong><br \/>\nThe Pythagorean theorem, involving the relationships between the sides of a right triangle, is one of the most famous geometry theorems.\u00a0 Many proofs have been generated to show the relationship, a<sup>2<\/sup>+b<sup>2<\/sup>=c<sup>2.<\/sup>.\u00a0 The a side and the b side are the legs on either side of the right angle, and the c side is the hypotenuse.<\/p>\n<p><strong>What Are Pythagorean Triples?<\/strong><br \/>\nFor example, suppose a right triangle is constructed with legs measuring 3 units and 4 units. Solving 3<sup>2 <\/sup>is 9, and 4<sup>2<\/sup> is 16. Adding 9 and 16 equals 25 .\u00a0 In turn, 25 equals 5<sup>2<\/sup>.\u00a0 The numbers 3, 4, and 5 are the first Pythagorean triple.\u00a0 In addition, 5<sup>2<\/sup> or 25 plus 12<sup>2 <\/sup>or 144 equals 169, or13<sup>2<\/sup>.\u00a0 Pythagorean triples were used in construction \u00a0<strong>very early in history.<\/strong><\/p>\n<p><strong>How Are the Sides Related?<\/strong><br \/>\nIf the length of the hypotenuse is known and either of the sides, the measurement of the other side can be found.\u00a0 In the above example, suppose the hypotenuse was 5 and one of the sides was 3.\u00a0 The measurement of the other side could be found by subtracting 25 &#8211; 9 = 16, and the square root of 16 is 4.<\/p>\n<p><strong>What Are Irrational Numbers?<\/strong><br \/>\nNot all\u00a0 sides of a right triangle are as neatly rational, however.\u00a0 Suppose the legs of a right triangle were each 1 unit.\u00a0 The hypotenuse would equal \u221a2, because if a<sup>2<\/sup>+b<sup>2<\/sup> = c<sup>2<\/sup>, c will equal \u221aa<sup>2<\/sup> +b<sup>2<\/sup>.\u00a0 That was shown with the Pythagorean triples.\u00a0 But \u221a2 is a decimal that is not very neat, with a nonrepeating decimal value starting with 1.4142.\u00a0 This was not as satisfying to the ancient Greeks, so they called those numbers &#8220;immeasurable.&#8221;<\/p>\n<p><strong>How Are Other Triangles Related?<\/strong><br \/>\nRight triangles are the only triangles with the relationship a<sup>2<\/sup> + b<sup>2<\/sup> = c<sup>2<\/sup>.\u00a0 However, other types of triangles have similar relationships among the sides of the triangle.\u00a0 If a<sup>2<\/sup> + b<sup>2<\/sup> &gt; c<sup>2<\/sup>, the triangle is acute.\u00a0 All its angles measure less than 90<sup>0<\/sup>.\u00a0 Similarly, if a<sup>2<\/sup> + b<sup>2<\/sup> &lt; c<sup>2<\/sup>, the triangle will have one angle that measures more than 90<sup>0<\/sup>.<\/p>\n<p>Interested in <a href=\"https:\/\/schooltutoring.com\/tutoring-programs\/math-tutoring\/\">math tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n<p><span class=\"tutorOrange\">SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Eugene, OR visit: <a href=\"https:\/\/schooltutoring.com\/tutoring-in-eugene-oregon\/\">Tutoring in Eugene, OR<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Overview: The Pythagorean theorem, involving the relationships between the sides of a right triangle, is one of the most famous geometry theorems.\u00a0 Many proofs have been generated to show the relationship, a2+b2=c2..\u00a0 The a side and the b side are the legs on either side of the right angle, and the c side is the [&hellip;]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[10],"tags":[902,1453,1715],"class_list":["post-6295","post","type-post","status-publish","format-standard","hentry","category-geometry","tag-hypotenuse","tag-pythagorean-theorem","tag-square-root"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6295","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=6295"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6295\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6295"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6295"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6295"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}