Question

Construct a $\Delta ABC$ in which AB = 6 cm, $\angle A={30}^{\circ }and\angle B={60}^{\circ }.$ Construct another $\Delta A{B}^{\prime }{C}^{\prime }\text{similar to}\Delta ABC$ with base AB' = 8 cm.

Answer 1

Scale factor
The required triangle can be drawn using the following steps:

1. Draw a ΔABC with side AB = 6 cm, ∠A = 30^o and ∠B = 60^o.

2. Draw a ray AZ making an acute angle with AB on the opposite side of vertex C.

3. Locate 4 points ( as 4 is greater in 4 and 3) A₁, A₂, A₃, and A₄ on AZ.

4. Join A₃B. Draw a line through A₄ parallel to A₃B intersecting extended AB at B^'.

5. Through B^', drawn a line parallel to BC intersecting ray AX at C'.

Hence, ΔAB'C' is the required triangle.