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      "body": "<p dir=\"auto\"></p>\n<div class=\"text-justify\">\nThe <em>Geometry</em> became a part of Mathematics that satisfied me as a teenage girl who filled her pencil case with colors and highlighters, I liked having that set of squares from the LION brand, because it came with its plastic case green in color and the edges were smooth. A true artist to make the lines, segments, triangles and other geometric figures that we drew to learn about <strong><div class=\"phishy\">reasons</div></strong> and <strong><div class =\"phishy\">proportions</div></strong> between 2 line segments.\n<p dir=\"auto\"></p>\n<p><center><img src=\"https://images.hive.blog/DQmYMk8wa56jFSG45rpPdtTz8BFiKHEGkEK5cnKaccJAwsA/imagen.png\" /></center></p>\n<div class=\"text-justify\">\n<p dir=\"auto\"></p>\nWhen we draw a straight line, we can indicate its <strong>length</strong> in any unit of measurement and we will refer to that continuous line of points as an unambiguous <strong>line</strong>. To use a nomenclature accepted throughout most of the world, we will write a lowercase <strong><div class=\"phishy\">r</div></strong> to refer to the line and we will include the values ​​for the endpoints of the line as <strong><div class=\"phishy\">P</div></strong> •────• <strong><div class=\"phishy\">Q</div></strong>\n<p dir=\"auto\"></p>\nWhen we try to divide that line into work sections, then we will refer to a <em>line segment</em> by placing a vinculum or a small dash over the pair of lowercase letters that we have assigned to the line segment, for example (<img src=\"https://images.hive.blog/DQmQx3b12BCRfrCpagcLBZZ9ZEjigxka1PsKi78QhP3Qwtd/imagen.png\" />)\n<p dir=\"auto\"></p>\nI am going to use the <a href=\"https://www.geogebra.org/geometry\" target=\"_blank\" rel=\"nofollow noreferrer noopener\" title=\"This link will take you away from hive.blog\" class=\"external_link\">Geogebra</a> graphic tool to explain this topic of the ratio and proportion of 2 line segments. Let the 2 segments be:\n<center>ab = 5 cm</center>\n<center>cd = 7 cm</center>\n<p dir=\"auto\"></p>\n<p dir=\"auto\"><center><img src=\"https://images.hive.blog/DQmbjjCeJwwqLHRzk8DeoQnRgHdikpSpwf25MNdsJzdyUZS/imagen.png\" /></center></p>\nNote that I do not include the link above the letters of each segment because this editing format does not allow it. The <strong>RATIO</strong> is the division between the lengths of 2 line segments, it is frequently expressed in terms of fractions. The first segment (ab) corresponds to 5 cm of the 7 cm of the second segment (cd), usually the larger number is placed in the denominator.\n<p dir=\"auto\"></p>\n<center><img src=\"https://images.hive.blog/DQmNPNRXzsk58qVmXNUbtK6UmTFUb7hDNc2MKboYU6paStc/imagen.png\" /></center>\n<p dir=\"auto\"></p>\nWe can also continue to expand the study of other segments and present a fraction that gives us an account of the <em> ratio</em>  between this new pair of segments:\n<center>ef = 5/2 cm</center>\n<center>gh = 7/2 cm</center>\n<p dir=\"auto\"></p>\n<center><img src=\"https://images.hive.blog/DQmXTqz66f4MS1UhoF6qxQQhw7wrTyEmc4awzu9E2thtkVW/imagen.png\" /></center>\n<p dir=\"auto\"></p>\nThe ratio between these two segments, evidently smaller than segments (ab) and (cd), turn out to have the same relationship, <div class=\"phishy\">Ratio = 5/7</div>. \n<p dir=\"auto\"><center><img src=\"https://images.hive.blog/DQmejM9rQStK3sDVJ6Y6SVDxdX3y6eAv5h7HVKRuKqyaxVz/imagen.png\" /></center></p>\nSince the analysis of each pair of segments separately gives us the result of the length ratio <div class=\"phishy\">Ratio = 5/7</div>, then we are in the presence of an equality of proportions according to the ratio.\n<p dir=\"auto\"></p>\n<center><img src=\"https://images.hive.blog/DQmUaJYUk3XUd5BaHqTBUuGgoaP1dXdrAduwYkZXca35Fod/imagen.png\" /></center>\n<p dir=\"auto\"></p>\nThe first 2 segments are proportional to the last 2 segments studied, because they have the same length ratio.<p dir=\"auto\"></p>\n<center><img src=\"https://images.hive.blog/DQmZ7w4B1VTworCBEH8VN1xWUzPgYHPPMDNJA7pzuK6xZ69/imagen.png\" /></center>\nThis same principle of the ratio between a pair of segments can be expanded and applied to some geometric figures, such as: square, rectangle, triangle, etc.<p dir=\"auto\"></p>\n<center><img src=\"https://images.hive.blog/0x0/https://i.picasion.com/pic92/be62700f1f3a01988b484d5ec7006c70.gif\" />\n</center><sup><a href=\"https://picasion.com/\" target=\"_blank\" rel=\"nofollow noreferrer noopener\" title=\"This link will take you away from hive.blog\" class=\"external_link\">https://picasion.com/</a></sup>\n<p dir=\"auto\"></p>\nWe draw a square of 2 cm on each side, AB = 2 cm, BC = 2 cm, CD = 2 cm and DA = 2 cm, then we set any coordinates (in this case (-1, -1)) of the center or focus for the proportional enlargement or reduction of this geometric figure taking as an example what was done with the ratio and proportion of straight line segments.<p dir=\"auto\"></p>\nIn this case it is called <div class=\"phishy\">Homothecy Ratio</div> (k), where each side of the original figure is going to be multiplied by this value (k), resulting in the geometric figure of a square increased by a value of 2, which was the homothecy ratio that I imposed on the example.\n<p dir=\"auto\"></p>\n<center><img src=\"https://images.hive.blog/DQmcUB882sWgkj3iB6fjPFLxUF8Yd8LR4Dfo6LW8aiZMGDK/imagen.png\" /></center>\n<p dir=\"auto\"></p>\nFinally, I present the case of proportionality by the homothecy ratio of a triangle with sides: AB = 2 cm, BC = 2 cm and CA = 2.8 cm.<p dir=\"auto\"></p>\n<center><img src=\"https://images.hive.blog/DQmUBhUzemssd6bMjcbsqvC3YEyECx6bjKbRM78HMC3XEAT/imagen.png\" /></center><p dir=\"auto\"></p>\n<h3><strong>Bibliographic support and image source</strong></h3><p dir=\"auto\"></p>\n<p dir=\"auto\">Our ideas and knowledge on the subject discussed in this article can be expanded voluntarily by consulting the following catalogue of references:</p>\n<ul>\n<li>Geogebra Calculator: <a href=\"https://www.geogebra.org/graphing?lang=es\" target=\"_blank\" rel=\"nofollow noreferrer noopener\" title=\"This link will take you away from hive.blog\" class=\"external_link\">Linear function cover</a></li>\n<li>Wikipedia: <a href=\"https://es.wikipedia.org/wiki/Vinculum_(s%C3%ADmbolo)\" target=\"_blank\" rel=\"nofollow noreferrer noopener\" title=\"This link will take you away from hive.blog\" class=\"external_link\">Vinculum</a></li>\n<li>Blog: <a href=\"http://dibujo.ramondelaguila.com/?page_id=362\" target=\"_blank\" rel=\"nofollow noreferrer noopener\" title=\"This link will take you away from hive.blog\" class=\"external_link\">Straight alphabet</a></li>\n<li>Wikipedia: <a href=\"https://es.wikipedia.org/wiki/Segmento\" target=\"_blank\" rel=\"nofollow noreferrer noopener\" title=\"This link will take you away from hive.blog\" class=\"external_link\">Segment</a></li>\n<li>Virtual program: <a href=\"https://www.geogebra.org/geometry\" target=\"_blank\" rel=\"nofollow noreferrer noopener\" title=\"This link will take you away from hive.blog\" class=\"external_link\">Geogebra</a></li>\n<li>Blog: <a href=\"https://edu.gcfglobal.org/es/fraccionarios/las-proporciones/1/\" target=\"_blank\" rel=\"nofollow noreferrer noopener\" title=\"This link will take you away from hive.blog\" class=\"external_link\">The proportions</a></li>\n<li>Blog: <a href=\"https://matemathweb.com/aritmetica/razones-y-proporciones/\" target=\"_blank\" rel=\"nofollow noreferrer noopener\" title=\"This link will take you away from hive.blog\" class=\"external_link\">Ratios and proportions</a></li>\n</ul>\n<p dir=\"auto\"></p>\n<center><strong>Graphical representation,</strong><br />\n<em>remains a powerful tool<br />\nwhen teaching Mathematics classes</em></center>\n<p dir=\"auto\"></p></div>",
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