show that the medians and certroid of a triangle using an activity
Answers
Answer:
A centroid of a triangle is the point where the three medians of the triangle meet. A median of a triangle is a line segment from one vertex to the mid point on the opposite side of the triangle. ... Once you have found the point where it will balance, that is the centroid of that triangle.
Answer:
A centroid of a triangle is the point where the three medians of the triangle meet. A median of a triangle is a line segment from one vertex to the mid point on the opposite side of the triangle. ... Once you have found the point where it will balance, that is the centroid of that triangle.
Step-by-step explanation:
To find the centroid of a given triangle by the method of paper folding
Materials Required
A sheet of white paper
A geometry box
Theory
The median of a triangle corresponding to any side is the line segment joining the midpoint of that side with the opposite vertex. The medians of a triangle are concurrent. The point of intersection of all the three medians of a triangle is called its centroid. Since all the medians meet at a single point, it is sufficient to find the point of intersection of only two medians to obtain the centroid of a triangle.
Procedure
Step 1: Draw any triangle ABC on the sheet of white paper. We have to find the centroid of this triangle.
Step 2: Fold the paper along the line that passes through the point A and cuts the line BC such that the point B falls on the point C. Make a crease and unfold the paper. Draw a line X1Y1 along the crease. Label the point D where the line X1Y1 intersects the line BC.
Then, AD is the median of ΔABC corresponding to ,the side BC as shown in Figure 15.1.
Math Labs with Activity - Find the Centroid of a Given Triangle 1
Step 3: Fold the paper along the line that passes through the point B and cuts the line AC such that the point A falls on the point C. Make a crease and unfold the paper. Draw a line X2Y2 along the crease. Label the point E where the line X2Y2 intersects the line AC. Then, BE is the median of ΔABC corresponding to the side AC as shown in Figure 15.2.
Math Labs with Activity - Find the Centroid of a Given Triangle 2
Step 4: Label the point O where the median AD intersects the median BE.
Observation
The point O where the two medians AD and BE of the given triangle ABC intersect is the centroid of ΔABC.
Result
The point O is the centroid of the given triangle ABC. Remark The teacher must ask the students to find the centroid of an obtuse-angled triangle and also of a right-angled triangle following the method described above.