Centroid of Triangle Working Model

Step by step 8 steps

1. 1

   Draw and cut out an acute, a right-angled and an obtuse triangle, each with sides of 15 to 25 cm, so you can show the result holds for every type.

2. 2

   On the first triangle, measure each side, mark its midpoint, and join each midpoint to the opposite corner: these are the three medians. They meet at one point; label it G.

3. 3

   Stretch coloured thread along each median between drawing pins at the corner and the midpoint, so the three threads visibly cross at G.

4. 4

   Measure both parts of each median, from the corner to G and from G to the midpoint, and write them on the triangle; each pair should be close to 2 : 1.

5. 5

   Balance the triangle on the stand's point at G: it stays level, because the centroid is the centre of mass of a uniform triangular sheet.

6. 6

   Find G on the second triangle without drawing medians: make a small hole near each corner, hang it from a pin on the cork board with the plumb line beside it, and draw along the thread. Repeat from the other two corners; the three lines meet at G.

7. 7

   Glue the right-angled triangle onto graph paper with its right angle at the origin, for example with corners at (0, 0), (15, 0) and (0, 18). Check that G = ((x₁ + x₂ + x₃) ÷ 3, (y₁ + y₂ + y₃) ÷ 3) = (5, 6) lands where its medians cross.

8. 8

   Mount all three triangles on a board with a heading, and add a card showing that the medians cut the triangle into six small triangles of equal area.