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The Median Of A Triangle Divides It Into Two Triangles Of Equal Area

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The Median Of A Triangle Divides It Into Two Triangles Of Equal Area. Put another way the centroid divides each median into two segments whose lengths are in. Ar ABD ar ACD Construction.

Geometry Problem 1246 Triangle Orthocenter Altitude Midpoint Perpendicular Geometry Problems Geometry Math Geometry
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Showing that the three medians of a triangle divide it into six smaller triangles of equal area. The median of a triangle divides it into triangle of equal area. Consider triangle BDC Area of triangle BDC 12 base height 12 DC AE -----3 From 1 2 and 3 we come to know that Area of triangle ABD Area of triangle DBC Therefore a median divides a triangle into two triangles of equal area.

Draw line AN BC Proof.

From the diagram in figure 1 we see that the two triangles CMA and BCM are equal in area. Brief discussion of the centroid as well. The centroid is exactly two-thirds the way along each median. If AB 1 and AF AD find the length of the line segment CE.

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