Name: Division of Line Segment in Given Ratio Externally
Uploaded: 2019-07-19
Duration: 5 min 53 s
Description: Line segments can also be divided by a point, not on the line. In this video, you will learn how to divide a line segment externally in some ratio, using a r...

Question

Construct a triangle with sides

6 cm, 7 cm and 8 cm

and then construct another triangle whose sides are

\frac{3}{4}

of the corresponding sides of the constructed triangle.

Accepted Answer

Given that, the three sides of a triangle are $6 cm, 7 cm and 8 cm$ and scale factor $= \frac{3}{4}$ .
We have to construct a triangle $A B C$ and a similar triangle $A' B C'$ , in which each side of $△ A' B C'$ is $\frac{3}{4} th$ of corresponding sides of $△ A B C$ .

Step of construction:

Step $1$ . Take $B C = 8 cm$ .

Step $2$ . From point $B$ draw an arc of $7 cm$ and from point $C$ draw an arc of $6 cm$ , cutting each other at point $A$ .

Step $3$ . Join $A B$ and $A C$ . Then $A B C$ is the required triangle.

Step $4$ . On $6 cm, 7 cm and 8 cm$ draw an acute angle $∠ C B X$ downwards.

Step $5$ . Along $B X$ , mark $4$ points $B_{1}, B_{2}, B_{3}$ and $B_{4}$ such that $B B_{1} = B_{1} B_{2} = B_{2} B_{3} = B_{3} B_{4}$ .

Step $6$ . Join $B_{4} C$ .

Step $7$ . From $B_{3}$ , draw $B_{3} C'$ parallel to $B_{4} C$ (draw an angle equal to $∠ B B_{4} C$ ), meeting $B C$ in $C'$ , such that $B C'$ is $\frac{3}{4}$ of $B C$ .

Step $8$ . From $C'$ , draw $A' C'$ parallel to $A C$ (draw an angle equal to $∠ A C B$ ), meeting $A B$ in $A'$ , such that $A' B$ is $\frac{3}{4}$ of $A B$ .

Then $△ A' B C'$ is the required triangle whose sides are $\frac{3}{4} th$ of the corresponding sides of the $△ A B C$ .

Construct a triangle with sides $6 cm, 7 cm and 8 cm$ and then construct another triangle whose sides are $\frac{3}{4}$ of the corresponding sides of the constructed triangle.

Important Questions on Constructions

Learn and Prepare for any exam you want !

Construct a triangle with sides 6 cm, 7 cm and 8 cm and then construct another triangle whose sides are 34 of the corresponding sides of the constructed triangle.

Important Questions on Constructions

Learn and Prepare for any exam you want !

Construct a triangle with sides $6 cm, 7 cm and 8 cm$ and then construct another triangle whose sides are $\frac{3}{4}$ of the corresponding sides of the constructed triangle.