Class 9 Exam > Class 9 Notes > Extra Documents & Tests for Class 9 > Procedure - To illustrate that the Internal Bisectors of the Angles of a Triangle Concur at a Point
Procedure - To illustrate that the Internal Bisectors of the Angles of a Triangle Concur at a Point | Extra Documents & Tests for Class 9 PDF Download
As performed in real lab:
Material required:
Coloured papers, fevicol and a pair of scissors.
Procedure:
1. Cut an acute angled triangle from a colored paper and name it as ABC.
2. Fold along the vertex A of the triangle in such a way that the side AB lies along AC.
3. The crease thus formed is the angle bisector of angle A. Similarly, get the angle bisectors of angle B and C. [Fig (a)].
4. Repeat the same activity for a obtuse angled triangle and right angled triangle. [Fig (b) and (c)].
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 vertex of the triangle to draw its angle bisector. You can use the protractor to measure the angles .
4.Activity completed successfully. You can see the inference below.
Observations:
-
We see that the three angle bisectors are concurrent and the point is called the incentre (O).
-
We observe that the incentre of an acute, an obtuse and right angled triangle always lies inside the triangle.
The document Procedure - To illustrate that the Internal Bisectors of the Angles 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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FAQs on Procedure - To illustrate that the Internal Bisectors of the Angles of a Triangle Concur at a Point - Extra Documents & Tests for Class 9
| 1. What is the definition of an internal bisector of an angle? |  |
Ans. An internal bisector of an angle is a line or ray that divides the angle into two congruent angles. It starts from the vertex of the angle and divides it into two equal parts.
| 2. How many internal bisectors does a triangle have? | |
Ans. A triangle has three internal bisectors, each corresponding to one of its angles. These internal bisectors intersect at a single point called the incenter of the triangle.
| 3. What is the significance of the point where the internal bisectors of a triangle intersect? | |
Ans. The point where the internal bisectors of a triangle intersect is called the incenter. This point is equidistant from all three sides of the triangle. It is also the center of the largest circle that can be inscribed within the triangle.
| 4. Can the internal bisectors of a triangle be extended beyond the triangle? | |
Ans. Yes, the internal bisectors of a triangle can be extended beyond the triangle. They will continue to divide the angles into two congruent angles even beyond the triangle's boundaries.
| 5. How can we prove that the internal bisectors of a triangle concur at a point? | |
Ans. To prove that the internal bisectors of a triangle concur at a point, we can use the angle bisector theorem. This theorem states that the ratio of the lengths of the segments formed by an angle bisector in a triangle is equal to the ratio of the lengths of the opposite sides of the triangle. By applying this theorem to each angle of the triangle, we can show that the three bisectors intersect at a single point.
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