write an activity to show Triangles : the Centroids .
Only written activity.
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Answers
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
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.