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A triangle is a three-sided, three-angled polygon. The sum of three internal angles of a triangle is 180 degrees. Moreover, based on side lengths, triangles can be classified into three types- equilateral, isosceles, and scalene triangles. Similarly, based on the angle measures, triangles are classified into three types that are right, acute, and oblique triangles. Along with that, the medians and altitudes of triangles are also two fundamental parts that students need to know to get a firm grip on geometry.
What is the Median of Triangles?
A median of a triangle is the line that joins a vertex of the triangle to the midpoint of the side opposite to the vertex of the triangle. Any triangle has three medians from its vertices.
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Here, triangle ABC has three medians, AD, BE, and CF.
Moreover, the median of isosceles triangle is perpendicular to the base of it. Furthermore, the median of isosceles triangle formula is given below.
Suppose, in triangle ABC, Angle A is joined to side ‘a’ of the triangle by the median, m. Thus, the formula for the median of triangle ABC will be:
m = √2b2 + 2c2 − a24
Besides knowing the formula of the median of an isosceles triangle, students also need to know some fundamental properties of it.
Median of a Triangle- Properties
Following are some key features of the medians of a triangle.
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The three medians of a triangle meet at a common point that is called the centroid of the triangle.
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Each median divides a triangle into two smaller triangles, and the areas of these smaller triangles are the same.
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In total, the three medians divide a triangle into six small triangles.
Now, let us proceed to the basic concept of altitude of a triangle as medians and altitudes of triangles both are crucial concepts to learn about a triangle.
What is Altitude of a Triangle?
An altitude is a line that starts from a vertex of a triangle and stretches till the opposite side of the triangle, forming a right angle with that side of the triangle.
Following is a diagram of an altitude of a triangle.
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Altitude of Triangle- Properties
The following are the features of an altitude of a triangle.
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Each triangle has three altitudes.
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These 3 altitudes connect at one point, and that is called the triangle’s ortho-center. Thus, all the medians and altitudes of triangles meet at a center point.
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It is the shortest distance between a base and a vertex of a triangle.
Median and Altitude of Isosceles Triangle
In the case of isosceles triangle median and altitude, there are some particular features to be learned. These features of the median and altitude of an isosceles triangle are as follows.
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Angle bisector and median both are the same in an isosceles triangle when an altitude is drawn from a vertex to base.
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Altitude median angle bisector all interchange in case of an isosceles triangle.
Nevertheless, besides this, medians and altitudes of triangles determine the type and property of the triangles. Hence, if you want to learn other relevant information regarding medians and altitudes of triangles, you can refer to the related study materials on Vedantu.
This leading e-learning platform provides a vast collection of study materials in all subjects, including mathematics. You can download the PDF version of the study materials. Moreover, they also conduct online classes that you can register for to clear your doubts about any topic from any subject.
Thus, download Vedantu’s App today and continue learning tips and tricks of geometry on the go!
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Source: Math Hello Kitty
Categories: Math
