# 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 it.

The steps involved in the required construction are:

1) Draw a line segment BC=6 cm.

2) Taking B as the center and radius 4 cm, draw an arc. Now taking C as the center and radius 5 cm draw another arc, intersecting the previous arc at A. Join AB and AC.

3) Draw any line segment BD, making an acute angle with BC and opposite to the vertex A. Taking B as the center and any radius, draw an arc, intersecting BD at E. Taking E as the center and radius BE, draw an arc, intersecting BD at F. Taking F as the center and radius BE, draw an arc, intersecting BD at G. Join CG.

4) Taking G as the center and any radius, draw an arc., intersecting BD and CG at H and I respectively. Taking F as the center and radius GH, draw an arc., intersecting BD at J. Taking J as the center and radius HI, draw an arc, intersecting previous arc at K. Join and extend FK, intersecting BC at L.

5) Taking C as the center and any radius, draw an arc., intersecting BC and CA at N and O respectively. Taking L as the center and radius CN, draw an arc., intersecting BC at P. Taking P as the center and radius NO, draw an arc, intersecting previous arc at Q. Join and extend LQ, intersecting AB at M.

6) ∆BLM is the required triangle.

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