Question

write an activity to show Triangles : the Centroids .

Only written activity.

No spam​

Answer 1

Answer:

As performed in real lab:

Materials required:

Coloured paper, pencil, a pair of scissors, gum.

Procedure:

From a sheet of paper, cut out three types of triangle: acute-angled triangle, right-angled triangle and obtuse-angle triangle.

For an acute-angled triangle, find the mid-points of the sides by bringing the corresponding two vertices together. Make three folds such that each Joins a vertex to the mid-point of the opposite side. [Fig (a)]

Repeat the same activity for a right-angled triangle and an obtuse-angled triangle. [Fig (b) and Fig (c)]

Acute-angled(a) Right-angled(b) Obtuse-angled(c)

As performed in the simulator:

Create a triangle ABC by providing three points A, B and C over the workbench.

Draw the mid-points of each line segment.

Click on each mid-points to draw their respective bisector lines.

You can see, Centroid lies inside the triangle for all acute angled, obtuse angled & right angled triangle.

Observations:

The students observe that the three medians of a triangle concur.

They also observe that the centroid of an acute, obtuse or right angled triangle always lies inside the triangle

Answer 2

The Centroid of a Triangle is the centre of the triangle that can be calculated as the point of intersection of all the three medians of a triangle.

The median is a line drawn from the midpoint of a side to the opposite vertex.

The centroid separates all the medians of the triangle in the ratio 2:1........

Where,

C is the centroid of the triangle.

x1,x2,x3 are the x-coordinate’s of the vertices of the triangle.

y1,y2,y3 are the y-coordinate’s of the vertices of the triangle.

Centroid of points, A, B and C is (x1+x2+x3)/3, (y1+y2+y3)/3.