CBSE Class 9 Mathematics Triangles Worksheet Set 03

Question 1. OBJECTIVE: To illustrate that the medians of a triangle are concurrent and the point of concurrency (centroid) always lies inside the triangle.
Answer: 1. Knowledge of different types of triangles.
2. Concept of median line segment.
3. Concept of concurrent lines.
4. Knowledge of obtaining the mid-point of a line segment by paper folding.
Procedure:
1. Take a coloured paper and cut an acute angled triangle \(ABC\) from this paper.
2. Fold the side \(BC\) of \(\Delta ABC\) keeping the point \(B\) exactly on the point \(C\) and press the fold such that the mid-point \(D\) of \(BC\) is obtained.
3. Similarly, repeat this process to find the mid-points \(E\) and \(F\) of other two sides \(AC\) and \(AB\) respectively.
4. Fold the \(\Delta ABC\) along \(AD\) and press the paper to get a clear crease.
5. Mark a line by a pen on this crease \(AD\) as a median of \(\Delta ABC\).
6. Similarly, obtain the other two medians \(BE\) and \(CF\).
7. Repeat the same activity for a right angled and an obtuse angled triangle.
Observation:
1. We observe that in each case, all the 3 medians pass through the same point (\(G\)) which shows that the medians of a triangle are concurrent.
2. The point of concurrency of the medians (the centroid) of the triangle always lies inside the triangle.
In simple words: The three medians of any triangle always meet at a single point called the centroid, and this point is always located inside the triangle regardless of the type of triangle.
Exam Tip: Remember that a median connects a vertex of a triangle to the mid-point of the opposite side, and the point where all three medians intersect is called the centroid.

Students must free download and practice these worksheets to gain more marks in exams. CBSE Class 9 Mathematics Worksheet - Triangles (2)