Math 2.0

Geometry Definition

Median of a triangle

Builds on TriangleMidpoint

Definition

Let ABCABC be a triangle in the Euclidean space ℝn\mathbb{R}^n. Let MAM_A be the midpoint of BB and CC. The median from AA is the segment { A+t(MA−A):t∈[0,1] }\{\, A + t (M_A - A) : t \in [0, 1] \,\} from AA to MAM_A. The medians from BB and from CC are defined in the same way, with the midpoints of CACA and of ABAB.

Remarks

Some texts call the whole line through AA and MAM_A the median. The three medians meet at the centroid. See the medians meet at the centroid. Each median divides the triangle into two triangles of equal area. Apollonius's theorem gives the length of a median from the side lengths.

Reading path

To understand this page from the ground up, read these 3 pages in order. The foundations come first.

Show the path as a graph
Midpoint, concept, no evidence levelMidpointconceptTriangle, concept, no evidence levelTriangleconceptMedian of a triangle, definition, no evidence levelMedian of a triangledefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Midpoint concept
  2. Triangle concept
  3. Median of a triangle definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Median_(geometry), lead section
About this page
Tag0ZET0ZH16W
URIm2://0ZET0ZH16W
Kinddefinition
WritingW1 stated
MSC51M04
DefinesMedian of a triangle
UsesTriangle, Midpoint

Markdown · JSON · Edit on GitHub

What this page needs for W2

  • edge instance_of in: one example (0 of 1)
  • edge not_instance_of in: one non-example that fails one clause (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

No page links to this page yet.