{"id":40,"date":"2015-01-28T01:30:32","date_gmt":"2015-01-28T08:30:32","guid":{"rendered":"https:\/\/blogs.ubc.ca\/symetrieducation\/?p=40"},"modified":"2015-01-28T01:30:32","modified_gmt":"2015-01-28T08:30:32","slug":"geometry-problem-solving-session-with-geogebra","status":"publish","type":"post","link":"https:\/\/blogs.ubc.ca\/symetrieducation\/2015\/01\/28\/geometry-problem-solving-session-with-geogebra\/","title":{"rendered":"Geometry problem-solving session with GeoGebra"},"content":{"rendered":"<p><a title=\"GeoGebra\" href=\"http:\/\/www.geogebra.org\" target=\"_blank\">GeoGebra<\/a> is a free, open-source interactive learning and teaching tool designed for all \u00a0levels of education. It is a dynamic software that can be used for algebra, geometry, statistics, calculus, and graphical analysis.\u00a0 GeoGebra is easy to learn and has an active international community of users, educators, and developers who support each other. It offers a rich set of tools and enables users to input geometric objects (points, lines, vectors, ellipses, etc.) and algebraic expressions (variables, functions, derivatives, integrals, etc.). Most importantly, it enables the students to manipulate these objects and expressions dynamically. GeoGebra can be downloaded and installed onto your computers and mobile devices or it can used used <a href=\"http:\/\/web.geogebra.org\/app\/\" target=\"_blank\">online<\/a>.<\/p>\n<p>Here is the geometry problem (<a href=\"http:\/\/www.math.ubc.ca\/~adler\/problems\/prob-4-12.pdf\" target=\"_blank\">Source: Dr. Andrew Adler, UBC<\/a>) that I posed in our 2015\/01\/13 SyMETRI meeting:<\/p>\n<p>Triangle ABC is right-angled at C. The bisector of &lt;ACB meets AB\u00a0at L. If BC = a<br \/>\nand AC = b, find the distance between the orthocenters of \u00a0triangles ALC\u00a0and BLC.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-47\" src=\"https:\/\/blogs.ubc.ca\/symetrieducation\/files\/2015\/01\/2015-01-28-00_03_04-DistanceBetweenOrthocenters.png\" alt=\"Triangle\" width=\"423\" height=\"278\" srcset=\"https:\/\/blogs.ubc.ca\/symetrieducation\/files\/2015\/01\/2015-01-28-00_03_04-DistanceBetweenOrthocenters.png 423w, https:\/\/blogs.ubc.ca\/symetrieducation\/files\/2015\/01\/2015-01-28-00_03_04-DistanceBetweenOrthocenters-300x197.png 300w\" sizes=\"auto, (max-width: 423px) 100vw, 423px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-49\" src=\"https:\/\/blogs.ubc.ca\/symetrieducation\/files\/2015\/01\/2015-01-28-00_12_38-DistanceBetweenOrthocenters.ggb_.png\" alt=\"Triangle\" width=\"423\" height=\"274\" srcset=\"https:\/\/blogs.ubc.ca\/symetrieducation\/files\/2015\/01\/2015-01-28-00_12_38-DistanceBetweenOrthocenters.ggb_.png 584w, https:\/\/blogs.ubc.ca\/symetrieducation\/files\/2015\/01\/2015-01-28-00_12_38-DistanceBetweenOrthocenters.ggb_-300x194.png 300w, https:\/\/blogs.ubc.ca\/symetrieducation\/files\/2015\/01\/2015-01-28-00_12_38-DistanceBetweenOrthocenters.ggb_-463x300.png 463w\" sizes=\"auto, (max-width: 423px) 100vw, 423px\" \/><\/p>\n<p>Hint: The distance between the orthocenters (O and P) involves a relationship between the sum and difference of the legs, and the\u00a0hypotenuse of the triangle.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>GeoGebra is a free, open-source interactive learning and teaching tool designed for all \u00a0levels of education. It is a dynamic software that can be used for algebra, geometry, statistics, calculus, and graphical analysis.\u00a0 GeoGebra is easy to learn and has &hellip; <a href=\"https:\/\/blogs.ubc.ca\/symetrieducation\/2015\/01\/28\/geometry-problem-solving-session-with-geogebra\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":28233,"featured_media":49,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[317],"tags":[7603],"class_list":["post-40","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math","tag-geogebra"],"_links":{"self":[{"href":"https:\/\/blogs.ubc.ca\/symetrieducation\/wp-json\/wp\/v2\/posts\/40","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ubc.ca\/symetrieducation\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ubc.ca\/symetrieducation\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/symetrieducation\/wp-json\/wp\/v2\/users\/28233"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/symetrieducation\/wp-json\/wp\/v2\/comments?post=40"}],"version-history":[{"count":9,"href":"https:\/\/blogs.ubc.ca\/symetrieducation\/wp-json\/wp\/v2\/posts\/40\/revisions"}],"predecessor-version":[{"id":51,"href":"https:\/\/blogs.ubc.ca\/symetrieducation\/wp-json\/wp\/v2\/posts\/40\/revisions\/51"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/symetrieducation\/wp-json\/wp\/v2\/media\/49"}],"wp:attachment":[{"href":"https:\/\/blogs.ubc.ca\/symetrieducation\/wp-json\/wp\/v2\/media?parent=40"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/symetrieducation\/wp-json\/wp\/v2\/categories?post=40"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/symetrieducation\/wp-json\/wp\/v2\/tags?post=40"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}