Construct a 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.

Sure, here are the steps to construct the triangles:

1. Draw a line segment AB of 4 cm.

2. With A as center and radius 5 cm, draw an arc.

3. With B as center and radius 6 cm, draw another arc intersecting the first arc at point C.

4. Join AC and BC to form the triangle ABC.

5. Now, to construct a triangle similar to ABC with sides 2/3 of the original, draw a line segment DE of length 2/3 * 4 cm = 2.67 cm.

6. With D as center and radius 2/3 * 5 cm = 3.33 cm, draw an arc.

7. With E as center and radius 2/3 * 6 cm = 4 cm, draw another arc intersecting the first arc at point F.

8. Join DF and EF to form the triangle DEF.

Now, triangle DEF is similar to triangle ABC and its sides are 2/3 of the corresponding sides of triangle ABC.