Draw a line segment of length 8 cm and divide it internally in the ratio 4: 5.
Steps of construction.

Construct an isosceles triangle with base 8 cm and altitude 4 cm. Construct another triangle whose sides are 2/3 times the corresponding sides of the isosceles triangle.

Draw a triangle ABC with BC = 6 cm, AB = 5 cm and ∠ABC 60. Then construct a triangle whose sides are 3/4 of the corresponding sides of the △ABC.

Construct a tangent of a circle of radius 4 cm from a point on the concentriccircle of radius 6 cm.

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

Construct a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then construct another triangle whose sides are 3/4 times the corresponding sides of the Δ ABC.

Draw a triangle ABC with side BC = 6 cm,  $\angle$C = 30⁰ and  $\angle$A = 105⁰. Then construct another triangle whose sides are $\frac{2}{3}$ times the corresponding sides of $∆$ABC.