{"id":4451,"date":"2016-10-01T10:05:28","date_gmt":"2016-10-01T10:05:28","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=4451"},"modified":"2017-06-14T12:13:09","modified_gmt":"2017-06-14T12:13:09","slug":"median-altitude-of-triangle","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/median-altitude-of-triangle\/","title":{"rendered":"What is the Median and Altitude of a Triangle"},"content":{"rendered":"
A closed figure bounded by three line segments is called a triangle.
\nIt is a 3-sided polygon and is named as ‘\u0394ABC’.
\nIn the above figure:
\n(a) Number of sides forming \u0394ABC are 3, i.e., AB, BC, and CA.
\n(b) Number of vertices (i.e., initial and terminal points of sides) are 3, i.e., A, B, and C.
\n(c) Number of angles are 3, i.e., \u2220A, \u2220B, and \u2220C.
\n(d) Sum of the angles of a triangle is 180\u00b0, i.e., \u2220A + \u2220B + \u2220C = 180\u00b0.
\nThe side AB is called the base line of \u0394ABC and the angle formed at vertex C opposite the base line AB is called the vertical angle.<\/p>\n
A triangle drawn on a plane divides the plane into 3 parts interior, exterior, and the triangle itself.
\n\u00a0The points lying inside \u0394ABC (i.e., cross) forms the interior of \u0394ABC and the points lying outside \u0394ABC (i.e., dots) forms the exterior of the \u0394ABC. Linear boundary of the triangle is the triangle itself.<\/p>\n
An altitude of a triangle is the line segment drawn from a vertex of a triangle, perpendicular to the line containing the opposite side. Notes : <\/strong><\/p>\n
\n(i) PS is an altitude on side QR in figure.
\n
\n(ii) AD is an altitude, with D the foot of perpendicular lying on BC in figure.
\n
\n(iii) The side PQ, itself is an altitude to base QR of right angled \uf044PQR in figure.
\n
\nNote:<\/strong>
\n(i) A triangle has three altitudes.
\n(ii) All the three altitudes meet at a point H (called orthocentre of triangle) i.e., all altitudes of any triangle are concurrent.
\n(iii) Orthocentre of the triangle may lie inside the triangle [Figure (i)],, outside the triangle [Figure (ii)] and on the triangle [Figure (iii)].
\n
\nOrthocentre
\n<\/strong>The point of concurrence of the altitudes of a triangle is called the orthocentre of the triangle.<\/p>\n\n