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subject: Geometry Median [print this page]

In this section we have geometry medianIn this section we have geometry median. The line-segment joining the vertex of a triangle to the middle point of the opposite side is called a geometric median. The geometry median splits the triangle into two equal parts of area. The triangle have three medians cross of position is labeled centroid. Each geometry median of length is divided by 1:2 ratios between the midpoint of median and the vertex.

Properties of the Median of Geometry:

The geometry median of a triangle everlastingly intersects within single point or centroid.

The geometry centroid forever lies within the triangle.

The geometry centroid splits the geometry median into two segments. The lengths of these two sections forever have a constant ratio.

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Geometry Median of Triangle Types:

For example,

Triangle

Consider a geometry triangle ABC.

Let A be the midpoint of BC, B be the midpoint of AC and C be the midpoint of AB , and O be the centroid.

Here, the above triangle geometry median:

Such as AA', BB' and CC'

Ratio of the geometry median: such as

A'O : OA 1 : 2

B'O : OB 1 : 2

C'O : OC 1 : 2

Bisection of triangle sides are,

AC' = C'B

AB' = B'C

BA' = A'C

Median types:

Geometry median concurrency conjecture (GMCC) defines that three medians of a triangle are concurrent. Each geometry median splits the triangle in half. The three geometry medians spilt the triangle into six minor triangles of equivalent area. Some other types of lines which spilt the region of the triangle into two identical parts do not pass through the centroid.

1. Acute triangle geometry median:

In acute triangle, the angle of A is below 90 degrees.

Let M be the geometry midpoint of BC, such as

/files/tvcs/acutemedian.png

In the above figure, the geometry median is AM and CM = MB. Therefore, the congruent of triangles are AMC and AMB.

2. Right triangle geometry median:

In right triangle, the angle of C is 90 degrees.

Let M be the geometry midpoint of AB, such as

Triangle

In the above figure, the geometry median is CM and AM = MB. Therefore, the congruent of triangles are CMA and CMB.

3. Obtuse triangle geometry median:

In an obtuse triangle, the angle of B is above 90 degrees.

Let M be the geometry midpoint of AC, such as

Triangle

In the above figure, the geometry median is BM and AM = MC. Therefore, the congruent of triangles are BMA and BMC.

by: johnharmer

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