{"id":6546,"date":"2013-12-02T17:26:09","date_gmt":"2013-12-02T17:26:09","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6546"},"modified":"2014-12-02T08:26:55","modified_gmt":"2014-12-02T08:26:55","slug":"math-review-of-the-triangle-inequality","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-the-triangle-inequality\/","title":{"rendered":"Math Review of the Triangle Inequality"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

Triangles have many different properties.\u00a0 For example, the sum of all three angles is always equal to 180o<\/sup>. The area of a triangle is equal to 1\/2 times the base times the height.\u00a0 The triangle inequality property is another property that can be used in real-world situations.<\/p>\n

Straight Lines and Triangles<\/strong><\/p>\n

Suppose A, B, and C are points that lie on a line.\u00a0 Then, the measurement of segment AB + the measurement of segment BC will equal the measurement of segment AC exactly.\u00a0 If segment AB = x and segment BC =y, segment AC will equal x +y.\u00a0 If points A, B, and C do not lie on the same line, the points will be the vertices of a triangle, and AB + BC will not equal AC.<\/p>\n

The Triangle Inequality<\/strong><\/p>\n

According to the triangle inequality principle, the sum of the length of any two sides of the triangle is greater than the third side.\u00a0 That means that for any triangle \u2206ABC, AB + BC \u2265AC, AC + BC \u2265AB , and AC + AB \u2265BC.\u00a0 Suppose the length of AB =x, the length of BC =y, and the length of AC = z. Then x +y >z, x +z >y, and y +z >x.<\/p>\n

Applying the Principle<\/strong><\/p>\n

Suppose side AB (or x) measures 15 units and side BC (or y) measures 22 units. That would leave 3 possible values.\u00a0 Either x +y >z , x +z >y, or y+z >x.\u00a0 Substituting the numbers for x and y, 15 +22 >z or 37>z.\u00a0 In the second inequality, 15 +z >22.\u00a0 If z > 22-15, z>7.\u00a0 The third inequality says that \u00a0\u00a022 + z> 15, which would make z>-7.\u00a0 The most meaningful statement is that z is between 7 and 37.<\/p>\n

How Is It Useful?<\/strong><\/p>\n

Sometimes it is enough to know that a value is between a range of numbers.\u00a0 A door on a hinge forms a triangle that has a minimum value and a maximum value.\u00a0 If that door is to be installed within a small space, it would be important to know that it could open and close freely.\u00a0 Suppose that a freezer has to fit in a pantry that has a clearance of 40 inches.\u00a0 If the hinge forms a triangle with the smallest value of 7 inches when it is nearly closed, and a maximum value when it is fully open of 37 inches, the freezer would fit in the pantry.\u00a0 If the pantry had a clearance of 30 inches, it would not fit, because the maximum value of 37 inches would be too large for the space.<\/p>\n

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Overview: Triangles have many different properties.\u00a0 For example, the sum of all three angles is always equal to 180o. The area of a triangle is equal to 1\/2 times the base times the height.\u00a0 The triangle inequality property is another property that can be used in real-world situations. Straight Lines and Triangles Suppose A, B, […]<\/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":[2,10],"tags":[1098,1854],"class_list":["post-6546","post","type-post","status-publish","format-standard","hentry","category-algebra","category-geometry","tag-measurement","tag-triangle-inequality-properties"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6546","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=6546"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6546\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6546"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6546"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6546"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}