November 10, 2008

This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Medians and Midsegment.

In this mini-lesson you’ll learn properties of medians and midsegments of triangles. Both these types of lines or line segments within triangles are concurrent, i.e. the three medians of a triangle share intersecting points, as do the three midsegments. The intersecting point is called the point of concurrency and these have special properties.

The medians of a triangle are the segments drawn from the vertices to the midpoints of the opposite sides and divide them in the ratio of 2 : 1. The point of intersection of all three medians is called the centroid of the triangle.

The centroid is always on the interior of the triangle. If the vertices of triangle*ABC* are *A*(*x*_{1}, *y*_{1}), *B*(*x*_{2}, *y*_{2}) and *C*(*x*_{3}, *y*_{3}), then coordinate of the centroid is {(*x*_{1} + *x*_{2} + *x*_{3})/3, (*y*_{1} + *y*_{2} + *y*_{3})/3}. For example, if the vertices of triangle *ABC* are *A*(2, 2), *B*(5, 2) and *C* (3, 4), then the centroid is ((2 + 5 + 3)/3, (2 + 2 + 4)/3) = (10/3, 8/3). Also the properties of medians are: the lengths of the medians of similar triangles are of the same proportion as the lengths of corresponding sides and the median of a right triangle from the right angle to the hypotenuse is half the length of the hypotenuse.

A midsegment of a triangle is a line segment connecting midpoints of two sides and is parallel to third side. It is half in length of third side. Every triangle has three midsegments. In a triangle*ABC*, if *D* is the mid point of *AC* and *E* is midpoint of *BC*, then line *DE* is the midsegment of triangle *ABC*, which is also parallel to *AB*. The measure of *DE* is half of *AB*. Midpoint is a point on a line segment that divides it into two equal parts. For example, if *A* (1, 2) and *C* (3, 5), then midpoint is ((1 + 3)/2, (2 + 5)/2) = (2, 7/2).

In this mini-lesson you’ll learn properties of medians and midsegments of triangles. Both these types of lines or line segments within triangles are concurrent, i.e. the three medians of a triangle share intersecting points, as do the three midsegments. The intersecting point is called the point of concurrency and these have special properties.

The medians of a triangle are the segments drawn from the vertices to the midpoints of the opposite sides and divide them in the ratio of 2 : 1. The point of intersection of all three medians is called the centroid of the triangle.

The centroid is always on the interior of the triangle. If the vertices of triangle

A midsegment of a triangle is a line segment connecting midpoints of two sides and is parallel to third side. It is half in length of third side. Every triangle has three midsegments. In a triangle

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

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