{"id":8959,"date":"2020-12-04T09:42:40","date_gmt":"2020-12-04T04:12:40","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=8959"},"modified":"2020-12-04T12:55:59","modified_gmt":"2020-12-04T07:25:59","slug":"proof","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/proof\/","title":{"rendered":"What is a Proof"},"content":{"rendered":"<h2><span style=\"color: #00ccff;\">What is a Proof<\/span><\/h2>\n<p>A <strong>proof<\/strong> is a written account of the complete thought process that is used to reach a conclusion. Each step of the process is supported by a theorem, postulate or definition verifying why the step is possible.<br \/>\nIn formal Euclidean proofs, no steps can be left out.<\/p>\n<p>If you think about the numerical problems you are used to solving in geometry, you will realize that your mind often does a &#8220;fast-forward&#8221; through some of the logical steps needed to reach a valid answer. In other words, you quickly &#8220;go right to the answer.&#8221;<br \/>\nCheck out the numerical problem below:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-123809 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-1.jpg\" alt=\"What is a Proof 1\" width=\"645\" height=\"269\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-1.jpg 645w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-1-300x125.jpg 300w\" sizes=\"(max-width: 645px) 100vw, 645px\" \/>You probably arrived at the answer of 6 long before you finished reading the explanation of the answer. Right?<\/p>\n<p>When developing a proof of this same problem, we must be careful to include ALL of the steps that led to our answer. We cannot &#8220;fast-forward&#8221; over steps when writing a proof. Check out the &#8220;proof&#8221; of this same problem:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-123810 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-2.jpg\" alt=\"What is a Proof 2\" width=\"612\" height=\"442\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-2.jpg 612w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-2-300x217.jpg 300w\" sizes=\"(max-width: 612px) 100vw, 612px\" \/>A proof requires that you document all of the little steps that you mentally &#8220;fast-forwarded&#8221; through in the numerical problem.<\/p>\n<p>What&#8217;s in a proof?<br \/>\nA formal 2-column proof contains the following components:<\/p>\n<ul>\n<li>Statement of the <strong>original problem<\/strong><br \/>\n<strong>Example:<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-123811\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-3.jpg\" alt=\"What is a Proof 3\" width=\"404\" height=\"128\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-3.jpg 404w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-3-300x95.jpg 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><br \/>\nThis information is usually stated in the original problem. \u00a0Some word problems, however, have to be dissected in order to get the specific information needed for the proof.<\/li>\n<li>Diagram, marked with &#8220;<strong>Given<\/strong>&#8221; information<br \/>\n<strong>Example:<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-123813\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-4.jpg\" alt=\"What is a Proof 4\" width=\"161\" height=\"131\" \/><br \/>\nThe diagram usually is not marked, so this step is very important. You will see the sought after congruent triangles and their corresponding parts much clearer with the diagram marked.<\/li>\n<li><strong>Re-statement<\/strong> of the &#8220;Given&#8221; information in the proof<br \/>\n<strong>Example:<br \/>\n<\/strong>\\(\\overline { AD }\\) \u2245 \\(\\overline { AB }\\), \u22211\u2245 \u22212<br \/>\nStating of the &#8220;given&#8221; information is almost always the first statement, and the reason is simply GIVEN.<\/li>\n<li>Complete <strong>supporting reasons<\/strong> for each step in the proof<br \/>\n<strong>Example:<\/strong><br \/>\n1. Given<br \/>\n2. Reflexive Property<br \/>\n3. SAS: If 2 sides and the include angle one triangle are congruent respectively to 2 sides and the included angles of a second triangle, then the 2 triangles are congruent.<br \/>\n4. Corresponding parts of congruent triangles are congruent.<br \/>\nThese supporting &#8220;reasons&#8221; vary between textbooks (and teachers), so be careful to follow the guidelines set by your teacher.<\/li>\n<li>The &#8220;<strong>Prove<\/strong>&#8221; statement as the last statement<br \/>\n<strong>Example:<br \/>\n<\/strong>\\(\\overline { CD }\\) \u2245 \\(\\overline { CB }\\)<br \/>\nThe &#8220;PROVE&#8221; is always the final statement. This statement is the purpose for the entire problem.<\/li>\n<\/ul>\n<p><strong>A Successful Strategy:\u00a0<\/strong><strong>Backwards Looking<\/strong><\/p>\n<p>For most proof problems, it is very helpful to examine the problem backwards &#8212; from the &#8220;Prove&#8221; statement back to the &#8220;Given&#8221; information. Let&#8217;s look at an example:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-123816\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-5.jpg\" alt=\"What is a Proof 5\" width=\"490\" height=\"126\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-5.jpg 490w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-5-300x77.jpg 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\nA Backwards Look &#8212; Where does the conclusion come from?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-123818\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-7.jpg\" alt=\"What is a Proof 7\" width=\"511\" height=\"121\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-7.jpg 511w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-7-300x71.jpg 300w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><br \/>\nBy looking at the above steps, we can see how to proceed with the proof. You might want to consider jotting down your &#8220;backward&#8221; thoughts before you begin writing your proof.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-123817\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-6.jpg\" alt=\"What is a Proof 6\" width=\"593\" height=\"281\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-6.jpg 593w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/What-is-a-Proof-6-300x142.jpg 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is a Proof A proof is a written account of the complete thought process that is used to reach a conclusion. Each step of the process is supported by a theorem, postulate or definition verifying why the step is possible. In formal Euclidean proofs, no steps can be left out. If you think about &#8230; <a title=\"What is a Proof\" class=\"read-more\" href=\"https:\/\/cbselibrary.com\/proof\/\" aria-label=\"More on What is a Proof\">Read more<\/a><\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[3275],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v18.4.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What is a Proof - CBSE Library<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cbselibrary.com\/proof\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is a Proof\" \/>\n<meta property=\"og:description\" content=\"What is a Proof A proof is a written account of the complete thought process that is used to reach a conclusion. 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