Question
Construct a $\triangle\text{ABC},$ in which BC = 6.5cm, AB = 4.5cm and $\angle\text{ABC}=60^\circ.$ Construct a triangle similar to this triangle whose sides are $\frac{3}{4}$ the corresponding sides of $\triangle\text{ABC}.$
✓
Answer
Steps of Construction:
- Draw a line segment BC = 6.5cm
- At B, construct $\angle\text{CBX}=60^\circ$
- With B as center and radius 4.5cm, draw an arc intersecting BX at A
- Join AC to obtain $\triangle\text{ABC}$
- Below BC, make an acute $\angle\text{CBY}$
- Along $B Y$, mark off 4 points (greater of 3 and in $\frac{3}{4}$ ) $B_1, B_2, B_3, B_4$ such that $B B_1=B_1 B_2=B_2 B_3=B_3 B_4$
- Join $B_4 C$
- From point $B_3$, draw a line parallel to $B_4 C$ intersecting $B C$ at $C^{\prime}$
- From Point C', draw a line parallel to AC intersecting AB at A'
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