Construct a triangle similar to a Δ XYZ with its sides equal to ( )th of the corresponding sides of ΔXYZ. It is given that XY = 6cm, XZ = 5 cm and ZY = 4 cm. Write the steps of construction.

Step 1: Draw a line segment XY = 6 cm.

Step 2: Taking X as center, draw an arc of radius 5 cm. Then, take Y as center and draw an arc of radius 4 cm. These arcs will intersect at point Z (say). Join XZ and YZ, such that XZ = 5 cm and ZY = 4 cm. Thus, ∆XYZ is the required triangle.

Step 3: Draw a ray XA making acute angle with straight line XY to the opposite side of vertex Z.

Step 4: Locate 4 points on ray XA, namely X ₁ , X ₂ and X ₃ (since 4 is greater among 3 and 4) such that, XX ₁ = X ₁ X ₂ = X ₂ X ₃ = X ₃ X ₄ .

Step 5: Join YX ₄ and then draw a line through X ₃ such that it is parallel to YX ₄ and intersects on XY at Y’.

Step 6: Now draw a line through Y’ such that it is parallel to YZ and intersects on XZ at Z’.

∆XY’Z’ is the required triangle with sides 3/4 of the corresponding sides of ∆XYZ.