Procedure - To illustrate that Perpendicular Bisectors of the Sides of a Triangle Concur at a Point

Procedure - To illustrate that Perpendicular Bisectors of the Sides of a Triangle Concur at a Point | Extra Documents & Tests for Class 9 PDF Download

As performed in the real lab

Material Required:

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

Procedure:

1. Cut an acute angled triangle from a coloured paper and name it as ABC.

2. Form the perpendicular bisector EF of AB using paper-folding method.

3. Similarly get the perpendicular bisectors GH and IJ of the sides AC and BC respectively.

4. Repeat the activity for right and obtuse angled triangles.

As performed in the simulator

1. Select three points A, B and C anywhere on the workbench  to draw a triangle.

2. Depending on your points selection acute, obtuse or right angled triangle is drawn.

3. Now, click on each mid-point to draw their respective perpendicular bisectors. You can use the scale to figure out mid point of each side.

4. Activity completed successfully. You can see the inference.

Observations:

•  The students see that the three perpendicular bisectors (the three creases obtained) are concurrent.

•  For the acute angled triangle, the circumcentre lies inside the triangle as shown in Fig(a).

•  For the right angled triangle, the circumcentre is the mid-point of the hypotenuse as shown in Fig(b)

•  For the obtuse angled triangle, the circumcentre lies outside the triangle as shown in Fig(c).

The document Procedure - To illustrate that Perpendicular Bisectors of the Sides of a Triangle Concur at a Point | Extra Documents & Tests for Class 9 is a part of the Class 9 Course Extra Documents & Tests for Class 9.
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Extra Documents & Tests for Class 9

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FAQs on Procedure - To illustrate that Perpendicular Bisectors of the Sides of a Triangle Concur at a Point - Extra Documents & Tests for Class 9

 1. How do you prove that the perpendicular bisectors of the sides of a triangle intersect at a single point?
Ans. To prove that the perpendicular bisectors of the sides of a triangle intersect at a single point, we can use the property that the perpendicular bisector of a line segment is equidistant from the endpoints of the segment. By constructing the perpendicular bisectors of each side of the triangle and showing that they are concurrent at a single point, we can prove this statement.
 2. What is the significance of the point of concurrency of the perpendicular bisectors in a triangle?
Ans. The point of concurrency of the perpendicular bisectors in a triangle is called the circumcenter. It is the center of the circumcircle, which is a circle passing through all three vertices of the triangle. The circumcenter plays an important role in various geometric constructions and calculations involving triangles.
 3. Can the perpendicular bisectors of the sides of a triangle be parallel?
Ans. No, the perpendicular bisectors of the sides of a triangle cannot be parallel. If the perpendicular bisectors were parallel, it would indicate that the sides of the triangle are equal in length, making it an equilateral triangle. However, in any non-degenerate triangle, the perpendicular bisectors intersect at a single point.
 4. How is the circumcenter of a triangle found using the perpendicular bisectors?
Ans. The circumcenter of a triangle can be found by constructing the perpendicular bisectors of the triangle's sides and finding their point of intersection. This point of concurrency is the circumcenter. It is equidistant from the three vertices of the triangle and lies on the perpendicular bisectors of each side.
 5. Can the perpendicular bisectors of a triangle be outside the triangle?
Ans. No, the perpendicular bisectors of a triangle cannot be outside the triangle. By definition, the perpendicular bisector of a side of a triangle passes through the midpoint of the side and is perpendicular to it. Therefore, the perpendicular bisectors must intersect within or on the boundary of the triangle, but not outside of it.

Extra Documents & Tests for Class 9

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