Following are the steps of the construction of the triangle of sides 4 cm, 5 cm, and 6 cm and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the first triangle.

1. Draw a line segment AB which measures 4 cm, i.e., AB = 4 cm.

2. Take point A as the center, and draw an arc of radius 5 cm.

3. Similarly, take point B as its center, and draw an arc of radius 6 cm.

4. The arcs drawn will intersect each other at point C.

 

Choose the next step from the following steps for the given construction.

Construction Procedure:-

1. Draw a line segment AB which measures 4 cm, i.e., AB = 4 cm.

2. Take point A as the center, and draw an arc of radius 5 cm.

3. Similarly, take point B as its center, and draw an arc of radius 6 cm.

4. The arcs drawn will intersect each other at point C.

5. Now, we have obtained AC = 5 cm and BC = 6 cm, and therefore, ΔABC is the required triangle.

6. Draw a ray AX which makes an acute angle with the line segment AB on the opposite side of vertex C.

7. Locate 3 points such as A1, A2, and A3 (as 3 is greater between 2 and 3) on line AX such that it becomes AA1= A1A2 = A2A3.

8. Join point BA3 and draw a line through A2, which is parallel to the line BA3 that intersects AB at point B’.

9. Through point B’, draw a line parallel to line BC that intersects the line AC at C’.

10. Therefore, ΔAB’C’ is the required triangle.