Draw a , right-angled at B such that AB = 3cm and BC = 4cm. Now, … - Vidyadip

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 $\angle\text{CBX}.$
Along $BX$, mark off 7 points $R_1, R_2, R_3, R_4, R_5, R_6, R_7$ such that $BR_1 = R_1R_2 = R_2R_3 = R_3R_4 = ... = R_6R_7$
Join $R_5C.$
From $R_7$, draw $R_7C_1 || R_5C$, meeting BC produced at $C_1.$
From $C_1$, draw $C_1A_1 || CA$, meeting BA 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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