#### Question

Construct a triangle similar to a given ΔXYZ with its sides equal to (3/4)^{th} of the corresponding sides of ΔXYZ. Write the steps of construction.

#### Solution

let XY = cm, YZ = cm and ∠Y = 60° and then a triangle similar to it whose sides are (3/4)^{th} of the corrosponding sides of ΔXYZ

we follow the following steps to construct triangle.

Step of construction

step 1. First of all we draw a line segment XY = 5 cm

step 2. With Y as centre on angle ∠Y = 60°

step 3. with Y as centre and radius YZ = 6 cm, draw on arc

step 4. Join XZ to obtain ΔXYZ

step 5. Below XY_{1} makes an acute angle ∠YXL = 60°

step 6. Below XL, mark off four points X_{1}, X_{2}, X_{3} and X_{4} such that XX_{1} = X_{1}X_{2} = X_{2}X_{3} = X_{3}X_{4}

step 7. Join X_{4}Y

step 8. since we have to construct a triangle each of whose sides is (3/4)^{th} of the corresponding sides of ΔXYZ

So, we take three parts out of four equal parts on XL from point X_{3} draw X_{3}Y' || X_{4}Y and meeting XY at Y'

step 9. From Y' draw Y'Z' || YZ, and meeting XZ at Z'

Hence, ΔXY'Z' is the required triangle, each of whose sides is (3/4)^{th} of the corresponding sides of ΔXYZ