Class 9 Exam > Class 9 Notes > Extra Documents & Tests for Class 9 > Procedure - To illustrate that the Medians of a Triangle Concur at a Point (called the Centroid)
Procedure - To illustrate that the Medians of a Triangle Concur at a Point (called the Centroid) | Extra Documents & Tests for Class 9 PDF Download
As performed in real lab:
Materials required:
Coloured paper, pencil, a pair of scissors, gum.
Procedure:
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From a sheet of paper, cut out three types of triangle: acute-angled triangle, right-angled triangle and obtuse-angle triangle.
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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)]
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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:
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Create a triangle ABC by providing three points A, B and C over the workbench.
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Draw the mid-points of each line segment.
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Click on each mid-points to draw their respective bisector lines.
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You can see, Centroid lies inside the triangle for all acute angled, obtuse angled & right angled triangle.
Observations:
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The students observe that the three medians of a triangle concur.
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They also observe that the centroid of an acute, obtuse or right angled triangle always lies inside the triangle.
The document Procedure - To illustrate that the Medians of a Triangle Concur at a Point (called the Centroid) | Extra Documents & Tests for Class 9 is a part of the Class 9 Course Extra Documents & Tests for Class 9.
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FAQs on Procedure - To illustrate that the Medians of a Triangle Concur at a Point (called the Centroid) - Extra Documents & Tests for Class 9
| 1. What is the definition of a centroid in a triangle? |  |
A centroid is a point of concurrency in a triangle where all three medians intersect. It is also known as the center of gravity or the center of mass of the triangle.
| 2. How many medians does a triangle have? | |
A triangle has three medians. Each median connects a vertex of the triangle to the midpoint of the opposite side.
| 3. Why do the medians of a triangle concur at a point? | |
The medians of a triangle concur at a point (centroid) because of the property of line symmetry. When a median is drawn, it divides the triangle into two smaller triangles with equal areas. The centroid is the point where the medians intersect, and it is the balancing point of the triangle.
| 4. What is the significance of the centroid in a triangle? | |
The centroid of a triangle has several significant properties. It divides each median into two segments, with the segment from the vertex to the centroid being twice as long as the segment from the centroid to the midpoint of the opposite side. The centroid is also the center of gravity of the triangle, which means that if the triangle is placed on a point, it will balance perfectly.
| 5. How can the centroid of a triangle be determined? | |
The centroid of a triangle can be determined by finding the average of the coordinates of the three vertices. For example, if the coordinates of the vertices are (x1, y1), (x2, y2), and (x3, y3), then the coordinates of the centroid would be ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).
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