Construct $\Delta ABC$ with $AB = 3 \, cm$,$BC = 6 \, cm$,and $AC = 5 \, cm$. Then,construct $\Delta BPQ$ similar to $\Delta ABC$ such that each side of $\Delta BPQ$ is $\frac{3}{4}$ of the corresponding sides of $\Delta ABC$. Write the steps of construction.
(N/A) Steps of construction:
$1$. Draw a line segment $BC = 6 \, cm$.
$2$. With $B$ as the center and radius $3 \, cm$,draw an arc. With $C$ as the center and radius $5 \, cm$,draw another arc intersecting the first arc at $A$.
$3$. Join $AB$ and $AC$ to obtain $\Delta ABC$.
$4$. Draw a ray $BX$ making an acute angle with $BC$ on the side opposite to vertex $A$.
$5$. Locate $4$ points $B_1, B_2, B_3, B_4$ on $BX$ such that $BB_1 = B_1B_2 = B_2B_3 = B_3B_4$.
$6$. Join $B_4C$.
$7$. Draw a line through $B_3$ parallel to $B_4C$ intersecting $BC$ at $Q$.
$8$. Draw a line through $Q$ parallel to $AC$ intersecting $AB$ at $P$.
$9$. $\Delta BPQ$ is the required triangle.
$1$. Draw a line segment $BC = 6 \, cm$.
$2$. With $B$ as the center and radius $3 \, cm$,draw an arc. With $C$ as the center and radius $5 \, cm$,draw another arc intersecting the first arc at $A$.
$3$. Join $AB$ and $AC$ to obtain $\Delta ABC$.
$4$. Draw a ray $BX$ making an acute angle with $BC$ on the side opposite to vertex $A$.
$5$. Locate $4$ points $B_1, B_2, B_3, B_4$ on $BX$ such that $BB_1 = B_1B_2 = B_2B_3 = B_3B_4$.
$6$. Join $B_4C$.
$7$. Draw a line through $B_3$ parallel to $B_4C$ intersecting $BC$ at $Q$.
$8$. Draw a line through $Q$ parallel to $AC$ intersecting $AB$ at $P$.
$9$. $\Delta BPQ$ is the required triangle.
Explore More
Similar Questions
To construct a triangle similar to a given $\triangle ABC$ with its sides being $\frac{8}{5}$ of the corresponding sides of $\triangle ABC$,a ray $BX$ is drawn such that $\angle CBX$ is an acute angle and $X$ is on the opposite side of $A$ with respect to $BC$. The minimum number of points to be located at equal distances on ray $BX$ is
Medium
View SolutionWrite 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 $AC$.
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 $AC$.
Difficult
View SolutionDraw $\Delta ABC$ with $AB = 5 \text{ cm}$,$BC = 6 \text{ cm}$,and $m\angle B = 90^{\circ}$. Then,construct $\Delta BPQ$ similar to $\Delta ABC$ such that its sides are $\frac{3}{2}$ times the corresponding sides of $\Delta ABC$. Write the steps of construction.
Medium
View SolutionGiven a rhombus $ABCD$ in which $AB = 4 \, cm$ and $\angle ABC = 60^{\circ}$,divide it into two triangles,$ABC$ and $ADC$. Construct a triangle $AB'C'$ similar to $\triangle ABC$ with a scale factor of $\frac{2}{3}$. Draw a line segment $C'D'$ parallel to $CD$,where $D'$ lies on $AD$. Is $AB'C'D'$ a rhombus? Give reasons.
Medium
View SolutionConstruct a triangle of sides $4 \, cm$,$5 \, cm$ and $6 \, cm$ and then a triangle similar to it whose sides are $\frac{2}{3}$ of the corresponding sides of the first triangle. Also,give the justification of the construction.
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo