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Mathematics
Special lines in a triangle
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Drag the three vertices to explore four families of special lines and their points of concurrency. Focus a vertex and use the arrow keys to move it.
Centroid G
Drag a vertex to reshape the triangle
Drag a vertex to reshape the triangle
Tab to handle A, B or C. Arrows: 0.1 unit; Shift or Page Up/Down: 0.5. Home/End: move to the valid left/right boundary. You can also select a vertex here and press “Move vertex”.
Acute triangle · scalene
Centroid G
The three medians meet at G. G divides each median in the ratio 2:1, measured from the vertex.
Inside
Join a vertex to the midpoint of the opposite side.
Ratio along the median
AG : GM = 2 : 1
- AG
- ≈ 4.06 u
- GM
- ≈ 2.03 u
Decimal measurements are rounded. Arbitrary length units.
A median is not necessarily perpendicular to the opposite side.
Model notes
- This is a plane Euclidean geometry model. Lines and intersections are calculated from the three vertices, using the same scale on both axes.
- Decimal measurements are rounded. Equal-length marks, right-angle marks and the ratio 2:1 express mathematical properties, not comparisons of rounded values.
- Dragging is limited to x from −6 to 6 and y from −4 to 6, with sides and altitudes at least 0.5 unit long. This keeps the drawing usable and does not limit the theorems.
- Only internal angle bisectors are shown. Altitudes meet the line containing the opposite side, including its extension. Observations from dragging do not replace a proof.