{"id":6945,"date":"2014-04-23T16:46:05","date_gmt":"2014-04-23T16:46:05","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6945"},"modified":"2014-12-02T08:25:30","modified_gmt":"2014-12-02T08:25:30","slug":"math-review-of-the-triangle-sum-property","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-the-triangle-sum-property\/","title":{"rendered":"Math Review of the Triangle-Sum Property"},"content":{"rendered":"

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

One of the many interesting properties of triangles is the Triangle-Sum Property.\u00a0 According to the Triangle-Sum property, the sum of the measures of the angles of any triangle is 180 degrees.\u00a0 The angles of the triangle form a straight angle.<\/p>\n

What Is a Triangle?<\/strong><\/p>\n

A triangle is a polygon that has three sides that are made of line segments, and three corners where those line segments meet.\u00a0 Triangles can be classified according to the lengths of their sides.\u00a0\u00a0Equilateral triangles have all three sides the same length, isosceles triangles have two sides the same length, and scalene triangles have none of the sides the same length.<\/p>\n

What about the Angles of a Triangle?<\/strong><\/p>\n

Triangles can also be classified by the measurements of their angles.\u00a0 Since equilateral triangles have all sides the same length, their interior angles also measure the same, 60\u00b0.\u00a0 Isosceles have two sides the same length and two angles the same measure.\u00a0 Scalene triangles do not have any angles the same.\u00a0 If each of the angles of a triangle measure less than 90\u00b0, then the triangle is called an acute triangle.\u00a0 Since an equilateral triangle has all three angles measuring 60\u00b0, and 60 is less than 90, all equilateral triangles are acute triangles.\u00a0 If a triangle has one angle that measures more than 90\u00b0, it is also called an obtuse triangle, because angles that measure more than 90\u00b0 are obtuse.\u00a0 If there are no angles of the triangle that measure 90\u00b0, it is an oblique triangle.<\/p>\n

What if One Angle of a Triangle Measures 90 Degrees?<\/strong><\/p>\n

Triangles that have one angle that measures 90\u00b0 are called right triangles.\u00a0 They have many unique properties, including that their sides follow the Pythagorean Theorem: a2<\/sup> + b2<\/sup> = c2<\/sup>, where the longest side c is also called the hypotenuse.\u00a0 Some of the special types of right triangles are the triangle whose sides measure 3 units, 4 units, and 5 units, because 32<\/sup> + 42<\/sup> = 52<\/sup>, and the right isosceles triangle whose angles measure 90\u00b0, 45\u00b0, and 45\u00b0.<\/p>\n

Why Does the Triangle-Sum Property Hold True?<\/strong><\/p>\n

The Triangle-Sum Property holds true for any type of triangle, whether equilateral, isosceles, or scalene.\u00a0 Suppose a line is drawn to \u2206ABC through point A, so that the line is parallel to segment BC.\u00a0 \u00a0It can be shown that all the lines form linear angles, so that the sum of those angles equals 180\u00b0.\u00a0 That means that if the measure of any two angles are known, the measure of the third angle of the triangle can be calculated.\u00a0 For example, suppose a scalene triangle has two angles with measurements of 100 and 37\u00b0.\u00a0 The third angle will measure 180\u00b0 – 100\u00b0 – 37\u00b0, or 43\u00b0.<\/p>\n

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Overview: One of the many interesting properties of triangles is the Triangle-Sum Property.\u00a0 According to the Triangle-Sum property, the sum of the measures of the angles of any triangle is 180 degrees.\u00a0 The angles of the triangle form a straight angle. What Is a Triangle? A triangle is a polygon that has three sides that […]<\/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":[10,13],"tags":[2683,992,1551,2684,2682],"class_list":["post-6945","post","type-post","status-publish","format-standard","hentry","category-geometry","category-pre-algebra","tag-equilaterial-triangles","tag-isosceles","tag-right-triangles","tag-scalene-triangles","tag-triangle-sum-property"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6945","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=6945"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6945\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6945"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6945"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6945"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}