CBSE Class 9 Mathematics Incentre Of A Triangle Worksheet Set 01

OBJECTIVE: To illustrate that the bisectors of angles of a triangle are concurrent and the point of concurrency (Incentre) always lies inside the triangle.

DESIGN AND OR APPROACH TO THE ACTIVITY:
1) Knowledge of different types of triangles.
2) Concept of concurrent lines.
3) Knowledge of obtaining the bisector of an angle by paper folding.

PROCEDURE:
1) Take a coloured paper and cut an acute angled triangle \(ABC\) from this paper.
2) Fold it along the vertex \(A\) such that \(AB\) coincides with \(AC\).
3) Now, press along the fold to form a crease. This crease represents the bisector of angle \(A\).
4) Similarly, obtain the creases representing the bisectors of angles \(B\) and \(C\).
5) Mark a line by a pen on these creases.
6) Repeat the same activity for a right-angled triangle and an obtuse angle triangle.

OBSERVATION:
1) It is observed that in each case, all the 3 angle bisectors pass through the same point (\(I\)) which shows that the bisectors of angles of a triangle are concurrent.
2) The point of concurrency of the bisectors of the angles of the triangle (the incentre) always lies inside the triangle.

Question 1. What is the point of concurrency of the angle bisectors of a triangle called?
Answer: The point of concurrency of the angle bisectors of a triangle is called the incentre.
In simple words: The incentre is the meeting point of all three interior angle bisectors of a triangle.

Exam Tip: Remember that the incentre is always equidistant from all three sides of the triangle and is the center of the inscribed circle (incircle).

Question 2. Does the incentre always lie inside the triangle for all types of triangles?
Answer: Yes, the incentre always lies in the interior of acute-angled, right-angled, and obtuse-angled triangles.
In simple words: Unlike the circumcentre or orthocentre, the incentre is never outside or on the boundary of a triangle; it is strictly internal.
Exam Tip: Always state that the interior angle bisectors intersect inside the region enclosed by the triangle, regardless of whether the triangle is acute, right, or obtuse.

Students must free download and practice these worksheets to gain more marks in exams. CBSE Class 9 Mathematics Worksheet - Incentre of a Triangle