{"id":5962,"date":"2013-05-23T03:32:32","date_gmt":"2013-05-23T03:32:32","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=5962"},"modified":"2014-12-02T08:27:01","modified_gmt":"2014-12-02T08:27:01","slug":"if-then-statements-in-geometric-proofs-and-computer-programs","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2013\/05\/23\/if-then-statements-in-geometric-proofs-and-computer-programs\/","title":{"rendered":"If-Then Statements in Geometric Proofs and Computer Programs"},"content":{"rendered":"

Overview:\u00a0 Mathematical Language<\/strong>
\nConditional statements, also called “if-then” statements are important in logic and mathematics.\u00a0 They state the antecedent as well as the consequent.\u00a0 The conditions are defined precisely in order to determine the parameters of the problem.\u00a0 In order for the entire statement to be correct, both sections must be true.<\/p>\n

Conditional Statements<\/strong>
\nGeometric proofs are usually stated in a shorthand that emphasizes rules and relationships.\u00a0 They use conditional statements, definitions, and postulates in a way that defines the connection between the hypothesis (the “if” portion) and its consequences (the “then” portion).\u00a0 For example, the statement, “If a figure is a square, then it must be a polygon” is only true if the given figure is both a square and that a square is a type of polygon.<\/p>\n

Instances and Counterexamples<\/strong>
\nWhile one instance, or even thousands of instances, of a statement being true does not necessarily prove it, only one counterexample will disprove it.\u00a0 Suppose the example were turned around such that the conditional statement read “If a figure is a polygon, then it must be a square.”\u00a0 That statement can be disproven with one counterexample.\u00a0 A triangle is a polygon, but it is not a square.<\/p>\n

Definitions and Postulates<\/strong>
\nBefore a conditional statement is made, definitions are given.\u00a0 For example, the figure is shown to have four sides of equal length that are perpendicular.\u00a0 In addition, polygons are defined as geometric figures that have three or more sides.\u00a0 If the reader didn’t know that the figure had four sides (the “if” portion), or what the definition of a polygon (the “then” portion, there wouldn’t be a way to connect the parts of the statement.\u00a0 Therefore, there wouldn’t be a way to find instances or counterexamples.\u00a0 Without a definition of the figure, the statement might be true or it might be false.\u00a0 What if the figure really had three sides and angles whose sum equaled 1800<\/sup>, but no one knew it?<\/p>\n

Computer Programs<\/strong>
\nConditional statements are essential in computer programs.\u00a0 They state the parameters of the problem in such a way that the computer can reach a conclusion.\u00a0\u00a0 Suppose a computer program is set up to calculate the number of diagonals in any polygon that has more than three sides.\u00a0 To define what the antecedent is, programmers will set up both parts of the conditional statement.\u00a0 If N \u2265 3, then solve N\u2219(N-3)\/2.<\/p>\n

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Overview:\u00a0 Mathematical Language Conditional statements, also called “if-then” statements are important in logic and mathematics.\u00a0 They state the antecedent as well as the consequent.\u00a0 The conditions are defined precisely in order to determine the parameters of the problem.\u00a0 In order for the entire statement to be correct, both sections must be true. Conditional Statements Geometric […]<\/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":[107,371,388,424,1061],"class_list":["post-5962","post","type-post","status-publish","format-standard","hentry","category-geometry","tag-antecedent","tag-conditional-statements","tag-consequent","tag-counterexamples","tag-logic"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5962","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=5962"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5962\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=5962"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=5962"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=5962"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}