**Question:**

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.

**Solution:**

Given that

Construct a triangle of sides $4 \mathrm{~cm}, 5 \mathrm{~cm}$ and $6 \mathrm{~cm}$ and then a triangle similar to it whose sides are $(2 / 3)$ of the corresponding sides of it.

We follow the following steps to construct the given

Step of construction

Step: I- First of all we draw a line segment.

Step: II- With *A *as centre and radius, draw an arc.

Step: III- With *B *as centre and radius, draw an arc, intersecting the arc drawn in step II at *C.*

Step: IV- Joins *AC *and *BC *to obtain.

Step: V- Below *AB, *makes an acute angle.

Step: VI- Along *AX,* mark off three points such that

Step: VII- Join.

Step: VIII- Since we have to construct a triangle each of whose sides is two-third of the corresponding sides of.

So, we take two parts out of three equal parts on *AX *from point draw and meeting *AB *at *C’.*

Step: IX- From *B’ *draw and meeting *AC *at *C’*

Thus, is the required triangle, each of whose sides is two third of the corresponding sides of*.*

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