Construct an equilateral triangle with each side $ 5 \mathrm{~cm} $. Then construct another triangle whose sides are $ 2 / 3 $ times the corresponding sides of $ \triangle A B C $.

Given:

An equilateral triangle of each side \( 5 \mathrm{~cm} \).

To do:

We have to construct an equilateral triangle with each side \( 5 \mathrm{~cm} \). Then construct another triangle whose sides are \( 2 / 3 \) times the corresponding sides of \( \triangle A B C \).

Solution:

Steps of construction:

(i) Draw a line segment $BC$ of length $5\ cm$.

(ii) Cut an arc of radius $5\ cm$ from point $B$ and an arc of $5\ cm$ from point $C$.

(iii) Name the point of intersection of arcs as point $A$. 

(iv) Now, join $AC$ and $BC$. $\Delta ABC$ is the required triangle.

(v) Draw a line $AX$ which makes an acute angle with $BC$ and is opposite of vertex $A$.

(vi) Cut three equal parts of line $AD$ namely $BB_1, BB_2, BB_3$.

(vii) Join $B_3$ to $C$. Draw a line $B_2C'$ parallel to $B_3C$

(viii) Now, draw a line $A'C'$ parallel to $AC$.

$\Delta BA'C'$ is the required triangle.

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Updated on: 10-Oct-2022

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