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...)
(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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ABC.
You’ll learn when move forward that triangles are classified mainly by its
sides and angles.
