{"id":5020,"date":"2012-12-03T22:08:55","date_gmt":"2012-12-03T22:08:55","guid":{"rendered":"http:\/\/schooltutoring.com\/scholarship\/?p=5020"},"modified":"2014-12-02T08:31:55","modified_gmt":"2014-12-02T08:31:55","slug":"concurrent-lines-and-point-of-concurrency","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/12\/03\/concurrent-lines-and-point-of-concurrency\/","title":{"rendered":"Concurrent Lines and Point of Concurrency"},"content":{"rendered":"

Concurrent lines all intersect at the same point, and all meet at a central location in a shape. How these are found, and calculated differ based on the individual shape. Let us explore how some shapes utilize concurrent lines.<\/p>\n

Medians-Centroid:<\/h5>\n

A line drawn from any vertex to the mid point of its opposite side is called a median with respect to that vertex. Thus, a triangle has 3 medians and all the 3 medians meet at one point. i.e. the medians of a triangle are concurrent.<\/strong><\/p>\n

The point of concurrency of medians is called centroid<\/em><\/strong> of the triangle.<\/p>\n

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Altitudes of a triangle:<\/h5>\n

A perpendicular line segment drawn from a vertex to its opposite side is called the altitude of the triangle with respect to that vertex. Thus, a triangle has 3 altitudes and all the 3 altitudes meet at one point. . i.e. the altitudes of a triangle are concurrent.<\/strong><\/p>\n

The point of concurrency of altitudes is called orthocenter<\/em><\/strong> of the triangle.<\/p>\n

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Angular Bisectors – Incenter:<\/h5>\n

The bisectors of the angles in atriangle meet at one point. i.e. the angular bisectors of a triangle are concurrent.<\/strong><\/p>\n

The point of concurrency of angular bisectors is called incenter<\/em><\/strong> of the triangle. If we draw a circle taking the incenter as the centre and the distance from the incenter to any side of the triangle as the radius then we get a circle which touches all the sides of the triangle which is known as the incircle<\/strong>.<\/p>\n

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Perpendicular Bisectors – Circumcenter:<\/h5>\n

A perpendicular bisector of a side of a triangle is a line which is perpendicular to the side and drawn at the mid point of the same side. There will be 3 perpendicular bisectors in a triang;e and all of them meet at one points. i.e. the perpendicular bisectors of a triangle are concurrent.<\/strong><\/p>\n

\u00a0\"\"<\/a><\/strong><\/p>\n

The point of concurrency of perpendicular bisectors is called circumcenter<\/em><\/strong> of the triangle. If we draw a circle taking the circumcenter as the centre and the distance from the circumcenter to any vertex of the triangle as the radius then we get a circle which touches all the vertices of the triangle which is known as the circumcircle<\/strong>.<\/p>\n

Need help with Standardized Tests?<\/a>?<\/p>\n

SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Nova-Scotia visit: Tutoring in Nova-Scotia. <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Concurrent lines all intersect at the same point, and all meet at a central location in a shape. How these are found, and calculated differ based on the individual shape. Let us explore how some shapes utilize concurrent lines. Medians-Centroid: A line drawn from any vertex to the mid point of its opposite side is […]<\/p>\n","protected":false},"author":19,"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":[199,365,960,1319,1347],"class_list":["post-5020","post","type-post","status-publish","format-standard","hentry","category-geometry","tag-bisector","tag-concurrency","tag-intersection","tag-perpendicular","tag-point"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5020","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\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=5020"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/5020\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=5020"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=5020"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=5020"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}