Write True or False and give reasons for your answer.
To construct a triangle similar to a given $\triangle ABC$ with its sides $\frac{7}{3}$ of the corresponding sides of $\triangle ABC$,draw a ray $BX$ making an acute angle with $BC$ and $X$ lies on the opposite side of $A$ with respect to $BC$. The points $B_{1}, B_{2}, \dots, B_{7}$ are located at equal distances on $BX$,$B_{3}$ is joined to $C$ and then a line segment $B_{6}C'$ is drawn parallel to $B_{3}C$ where $C'$ lies on $BC$ produced. Finally,line segment $A'C'$ is drawn parallel to $AC$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(B) False.
To construct a triangle similar to $\triangle ABC$ with a scale factor of $\frac{7}{3}$,we must divide the ray $BX$ into $7$ equal parts (since $7 > 3$).
Steps of construction:
$1.$ Draw a ray $BX$ making an acute angle with $BC$.
$2.$ Locate $7$ points $B_{1}, B_{2}, \dots, B_{7}$ on $BX$ such that $BB_{1} = B_{1}B_{2} = \dots = B_{6}B_{7}$.
$3.$ Join $B_{3}$ to $C$ (since the denominator is $3$).
$4.$ Draw a line through $B_{7}$ parallel to $B_{3}C$ intersecting the extended line segment $BC$ at $C'$.
$5.$ Draw a line through $C'$ parallel to $AC$ intersecting the extended line segment $BA$ at $A'$.
The given statement claims that $B_{6}C'$ is drawn parallel to $B_{3}C$,which is incorrect because the scale factor is $\frac{7}{3}$,requiring the parallel line to be drawn from $B_{7}$,not $B_{6}$.

Explore More

Similar Questions

Draw an equilateral triangle $ABC$ with each side $4\, cm$. Construct a triangle similar to it with a scale factor of $\frac{3}{5}$. Is the new triangle also equilateral?

Draw a parallelogram $ABCD$ in which $BC = 5 \, cm$,$AB = 3 \, cm$ and $\angle ABC = 60^{\circ}$. Divide it into triangles $BCD$ and $ABD$ by the diagonal $BD$. Construct the triangle $BD'C'$ similar to $\triangle BDC$ with a scale factor of $\frac{4}{3}$. Draw the line segment $D'A'$ parallel to $DA$,where $A'$ lies on the extended side $BA$. Is $A'BCD'$ a parallelogram?

Difficult
View Solution

Draw $\overline{XY}$ of length $9\, cm$ and divide it in the ratio $2:5$ from $X$. Write the steps of construction.

Difficult
View Solution

Draw $\Delta PQR$ with $m \angle P=60^{\circ}, m \angle Q=45^{\circ}$ and $PQ =6 \text{ cm}$. Then construct $\Delta PBC$ similar to $\Delta PQR$ whose sides have lengths $\frac{5}{3}$ times the lengths of the corresponding sides of $\Delta PQR$.

Draw a right triangle $ABC$ in which $BC = 12 \, cm$,$AB = 5 \, cm$ and $\angle B = 90^{\circ}$. Construct a triangle similar to it with a scale factor of $\frac{2}{3}$. Is the new triangle also a right triangle?

Difficult
View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo