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Constructions — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsConstructions5 Marks
Question
Draw a $\triangle\text{ABC},$ right-angled at B such that AB = 3cm and BC = 4cm. Now, Construct a triangle a triangle similar to $\triangle\text{ABC},$ each of whose sides is $\frac75\text{times}$ the correponding side of $\triangle\text{ABC}.$
✓

Answer


Steps of construction:
Draw a line segment BC = 4cm
AT B, construct $\angle\text{MBC}=90^\circ.$
Cut-off BA = 3cm from BM.
Join AC.
Thus, right-angled $\triangle\text{ABC}$ is obtained.
Below BC, make an acute $\angle\text{CBX}.$
6. Along $B X$, mark off 7 points $R_1, R_2, R_3, R_4, R_5, R_6, R_7$ such that $B R_1=R_1 R_2=R_2 R_3=R_3 R_4=\ldots=R_6 R_7$
7. Join $R _5 C$.
8. From $R_7$, draw $R_7 C_1 \| R_5 C$, meeting $B C$ produced at $C_1$.
9. From $C_1$, draw $C_1 A_1 \| C A$, meeting $B A$ produced at $A_1$.
Then, $\triangle\text{A}_1\text{BC}_1$ is the required triangle similar to $\triangle\text{ABC}$ such that each side of $\triangle\text{A}_1\text{BC}_1$ is $\frac75\text{times}$ the corresponding side of $\triangle\text{ABC}.$

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