This is a free lesson from our course in Geometry In this lesson you�ll be introduced to the concepts of Triangles and about using them. You�ll learn the related contents, explanations with examples in the presentation by instructor using video and in own hand writing. This will provide the geometry help; in context with triangles and applying the developed skills, for finding solution to real-world problems.
 A triangle is a polygon with three sides. The triangles are of different shapes and sizes and have many points, lines and circles in it.You�ll recall from earlier learning that sides of a triangle are marked often by small letters and corresponding to it designations of opposite vertices, marked in capital letters. (More text below video...) Other useful lessons:
 Triangles Classification Triangle Angle-Sum Theorem Triangle Inequality Medians and Midsegment
(Continued from above) Before moving to triangles classifications i.e. classify different forms of triangles, you should learn some of the essential features of a triangle. It is a polygon with three vertices and three sides or edges that are line segments. A triangle with vertices A, B, C is designated as triangle ABC and symbolically written as ABC. You�ll learn when move forward that triangles are classified mainly by its sides and angles.
properties of triangles
The fundamental and important properties of a triangle are:
� triangle is a three sided plane or two-dimensional figure
� the sum of the three angles of a triangle is always 180 � an exterior angle of a triangle, equals the sum of the two interior opposite angles
Salient lines and points of a Triangle
Altitude, also called height of a triangle, is a perpendicular dropped from any vertex to an opposite side. This side is called a �base� of triangle in this case. Three altitudes of triangle intersect at one point, called an �orthocenter-point O� of the triangle (Fig-1). Median is defined as the segment, joining any vertex of a triangle and a midpoint of the opposite side. Three medians of the triangle ABC- AD, BE, CF intersect in one point O (Fig-2) This point divides each median in the ratio 2:1, starting from the vertex.
Bisector is defined as a segment of the angle bisector, from the vertex to a point of intersection with an opposite side. Three bisectors of a triangle i.e. AD, BE, CF intersect at one point called �center of an inscribed circle� i.e. �O�.
Notice that a bisector divides an opposite side into two parts, in the ratio of the adjacent sides. E.g. AE: CE = AB: BC (Fig-3).
Midperpendicular is a perpendicular, drawn from a middle point of a side. Notice that three midperpendiculars of ABC (each drawn through the middle of its side i.e. points P, Q, R in Fig- 4), intersect at a point �O� which is the center of circle known as circumcircle. Remember: a triangle is one of the basic figures used in geometry. Like other figures in geometry, it helps to solve the real-life application problems � be it the structure of a bridge, constrictions of structures or holding up a shelf. Triangles also find use in reference to places that have similar to triangular shape, say example - the Bermuda Triangle.
The video above will explain more in detail about Triangles and relationship of the involved properties, with the help of several examples and practice problems.
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