Question
Construct a $\triangle\text{ABC}$ in which AB = 6cm, $\angle\text{A}=30^\circ$ and $\angle\text{B}=60^\circ.$ Construct another $\triangle\text{AB}'\text{C}'$similar to $\triangle\text{ABC}$ with base AB' = 8cm.
✓
Answer
Steps of Construction:
Step 1. Draw a line segment AB = 6cm.
Step 2. At A, draw $\angle\text{XAB}=30^\circ$
Step 3. At B, draw $\angle\text{YBA}=60^\circ.$ Suppose AX and BY intersect at C.
Thus, $\triangle\text{ABC}$ is the required triangle.
Step 4. Produce AB to B' such that AB' = 8cm.
Step 5. From B', draw B'C' || BC meeting AX at C'.
Here, $\triangle\text{AB}'\text{C}'$ is the required triangle similar to $\triangle\text{ABC}.$
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