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Constructions — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsConstructions5 Marks
Question
Construct a $\triangle\text{ABC}$ in which $BC = 8cm, $ $\angle\text{B}=45^\circ$ and $\angle\text{C}=60^\circ.$ Construct another triangle similar to $\triangle\text{ABC}$ such that its sides are $\frac35$ of the corresponding sides of $\triangle\text{ABC}.$
✓

Answer


Steps of Construction:
Step 1. Draw a line segment $BC = 8cm.$
Step 2. At $B$, draw $\angle\text{XBC}=45^\circ.$
Step 3. At $C,$ draw $\angle\text{YCB}=60^\circ.$ Suppose $BX$ and $CY$ intersect at $ A.$
Thus, $\triangle\text{ABC}$ is the required triangle.
Step 4. Below $BC,$ draw an acute angle $\angle\text{ZBC}.$
Step 5. Along $BZ, $ mark five points $Z_1, Z_2, Z_3, Z_4$ and $Z_5$ such that $BZ_1 = Z_1Z_2 = Z_2Z_3 = Z_3Z_4 = Z_4Z_5.$​​​​​​​
Step 6. Join $CZ_5$.
Step 7. From $Z_3,$ draw $Z_3C' || CZ_5$ meeting $BC$ at $C'.$​​​​​​​
Step 8. From $C',$ draw $A'C' || AC$ meeting $AB$ in $A'.$
Here, $\triangle\text{AB}'\text{C}'$ is the required triangle whose sides are $\frac{3}{5}$ of the corresponding sides of $\triangle\text{ABC}.$

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