Draw a parallelogram ABCD in which BC = 5cm, AB = 3cm and =60^ , … - Vidyadip

Question

Draw a parallelogram ABCD in which BC = 5cm, AB = 3cm and $\angle\text{ABC}=60^\circ,$ divide it into triangles BCD and ABD by the diagonal BD. Construct the triangle BD'C' similar to $\triangle\text{BDC}$ with scale factor $\frac{4}{3}.$ Draw the line segment D'A' parallel to DA where A' lies on extended side BA. Is A'BC'D' a parallelogram?

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Answer

Steps of construction:

1. Draw a line segment $A B=3 cm$.
2. Make $\angle A B C=60^{\circ}$ such that $B C=5 cm$.
3. Draw $C D \| A B$ and $A D \| B C, \square A B C D$ is the required parallelogram.
4. Join diagonal $B D$ and produce it.
5. Make acute angle $C B X$ on opposite of $D$ with respect to $B C$.
6. Mark (equi spaced) $B_1, B_2, B_3, B_4$ by compass.
7. Join $B_3 C$ and draw $B_3 C \| B_4 C^{\prime}$ on $B C$ produced.
8. Again, draw $C^{\prime} D^{\prime} \| C D$, where $D^{\prime}$ is on $B D$ produced.
9. Now, draw $D^{\prime} A^{\prime} \| D A$ where $A^{\prime}$ is on $B A$ produced. Parallelogram $A^{\prime} B C^{\prime} D^{\prime}$ is similar to parallelogram $A B C D$ with scale factor $\frac{4}{3}$.

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