Q8. - Geometry

Question

Draw any large $\Delta ABC$ and construct equilateral triangles on each of the sides as shown.

1. In each of the three equilateral triangles, construct any two medians and find their point of intersection.
2. Draw the three segments connecting these three points of intersection.
3. What appears tobe true about the triangle you drew in part (b)?

Step-by-Step Solution

Answer

The intersections of medians of a triangle forms a new equilateral triangle.

Step 1. Given information.

ABC triangle and extended three triangles are given.

Step 2. Concept Used.

Medians divide the midpoint in the ratio $2:1$ from the vertex to the side.

Step 3. Let’s construct.

Medians of the equilateral triangle, 

Upon joining all the medians of each triangle, we obtain a new equilateral triangle XYZ