Similar Triangles

In the following figure, point $\mathrm{D}$ divides $\mathrm{AB}$ in the ratio $3:5.$ Find:

$\mathrm{BC}=4.8\mathrm{cm},$ find the length of $\mathrm{DE}.$

In the following figure, point $\mathrm{D}$ divides $\mathrm{AB}$ in the ratio $3:5.$ Find:

$\mathrm{DE}=2.4\mathrm{cm},$ find the length of $\mathrm{BC}.$

In the following figure, point $\mathrm{D}$ divides $\mathrm{AB}$ in the ratio $3:5.$ Find:

$\frac{\mathrm{AE}}{\mathrm{AC}}$

In the given figure, $\angle \mathrm{B}=\angle \mathrm{E},$ $\angle \mathrm{ACD}=\angle \mathrm{BCE},$ $\mathrm{AB}=10.4\mathrm{cm}$ and $\mathrm{DE}=7.8\mathrm{cm}.$ Find the ratio between areas of the $△\mathrm{ABC}$ and $△\mathrm{DEC}.$

In the given figure, $\mathrm{ABC}$ is a triangle. $\mathrm{DE}$ is parallel to $\mathrm{BC}$ and $\frac{\mathrm{AD}}{\mathrm{DB}}=\frac{3}{2}.$

What is ratio of the areas of $∆\mathrm{DEF}$ and $∆\mathrm{BFC}$ ?

In the given figure, $\mathrm{ABC}$ is a triangle. $\mathrm{DE}$ is parallel to $\mathrm{BC}$ and $\frac{\mathrm{AD}}{\mathrm{DB}}=\frac{3}{2}.$

Prove that $∆\mathrm{DEF}$ is similar to $∆\mathrm{CBF}.$

Hence, find $\frac{\mathrm{EF}}{\mathrm{FB}}.$

In the given figure, $\mathrm{ABC}$ is a triangle. $\mathrm{DE}$ is parallel to $\mathrm{BC}$ and $\frac{\mathrm{AD}}{\mathrm{DB}}=\frac{3}{2}.$

Determine the ratio $\frac{\mathrm{AD}}{\mathrm{AB}}$ and $\frac{\mathrm{DE}}{\mathrm{BC}}.$

In the given figure, $\mathrm{BC},$ is parallel to $\mathrm{DE}.$ Area of triangle $\mathrm{ABC}=25{\mathrm{cm}}^2,$ Area of trapezium $\mathrm{BCED}=24{\mathrm{cm}}^2$ and $\mathrm{DE}=14\mathrm{cm}.$ Calculate the length of $\mathrm{BC}.$

Also, find the area of the triangle $\mathrm{BCD}.$

In the figure, given below, $\mathrm{ABCD}$ is a parallelogram. $\mathrm{P}$ is a point on $\mathrm{BC}$ such that $\mathrm{BP}:\mathrm{PC}=1:2.$ $\mathrm{DP}$ produced meets $\mathrm{AB}$ produced at $\mathrm{Q}.$ Given the area of triangle $\mathrm{CPQ}=20{\mathrm{cm}}^2.$

Calculate: Area of parallelogram $\mathrm{ABCD}.$

In the figure, given below, $\mathrm{ABCD}$ is a parallelogram. $\mathrm{P}$ is a point on $\mathrm{BC}$ such that $\mathrm{BP}:\mathrm{PC}=1:2.$ $\mathrm{DP}$ produced meets $\mathrm{AB}$ produced at $\mathrm{Q}.$ Given the area of triangle $\mathrm{CPQ}=20{\mathrm{cm}}^2.$

Calculate: Area of triangle $\mathrm{CDP}.$

The given diagram shows two isosceles triangles which are similar. In the given diagram, $\mathrm{PQ}$ and $\mathrm{BC}$ are not parallel;  $\mathrm{PC}=4,$ $\mathrm{AQ}=3,$ $\mathrm{QB}=12,$ $\mathrm{BC}=15$ and $\mathrm{AP}=\mathrm{PQ}.$

Calculate: The ratio of the areas of triangle  $\mathrm{APQ}$ and triangle $\mathrm{ABC}.$

The given diagram shows two isosceles triangles which are similar. In the given diagram, $\mathrm{PQ}$ and $\mathrm{BC}$ are not parallel;  $\mathrm{PC}=4,$ $\mathrm{AQ}=3,$ $\mathrm{QB}=12,$ $\mathrm{BC}=15$ and $\mathrm{AP}=\mathrm{PQ}.$

Calculate: The length of $\mathrm{AP}.$

In the given triangle $\mathrm{PQR}, \mathrm{LM}$ is parallel to  $\mathrm{QR}$ and $\mathrm{PM}:\mathrm{MR}=3:4.$

Calculate the value of ratio: $\frac{\mathrm{Area} \mathrm{of} ∆\mathrm{LQM}}{\mathrm{Area} \mathrm{of} ∆\mathrm{LQN}}$

In the given triangle $\mathrm{PQR}, \mathrm{LM}$ is parallel to  $\mathrm{QR}$ and $\mathrm{PM}:\mathrm{MR}=3:4.$

Calculate the value of ratio: $\frac{\mathrm{Area} \mathrm{of} ∆\mathrm{LMN}}{\mathrm{Area} \mathrm{of} ∆\mathrm{MNR}}$

In the given triangle $\mathrm{PQR}, \mathrm{LM}$ is parallel to  $\mathrm{QR}$ and $\mathrm{PM}:\mathrm{MR}=3:4.$

Calculate the value of ratio: $\frac{\mathrm{PL}}{\mathrm{PQ}}$ and then $\frac{\mathrm{LM}}{\mathrm{QR}}$

The ratio between the corresponding sides of two similar triangles is $2$ is to $5.$ Find the ratio between the areas of these triangles.

The given figure shows a parallelogram $\mathrm{ABCD}.$ $\mathrm{E}$ is a point in $\mathrm{AD}$ and $\mathrm{CE}$ produced meets $\mathrm{BA}$ produced at point $\mathrm{F}.$ If $\mathrm{AE}=4\mathrm{cm},$ $\mathrm{AF}=8\mathrm{cm}$ and $\mathrm{AB}=12\mathrm{cm},$ find the perimeter of the parallelogram $\mathrm{ABCD}$

In the following figure, $\mathrm{M}$ is midpoint of $\mathrm{BC}$ of a parallelogram $\mathrm{ABCD}.$ $\mathrm{DM}$ intersects the diagonal $\mathrm{AC}$ at $\mathrm{P}$ and produced at $\mathrm{E}.$ Prove that: $\mathrm{PE}=2\mathrm{PD}$.

In figure, given below, $\mathrm{PQR}$ is a right-angle triangle right angled at $\mathrm{Q}.$ $\mathrm{XY}$ is parallel to $\mathrm{QR},$ $\mathrm{PQ}=6\mathrm{cm},$ $\mathrm{PY}=4\mathrm{cm}$ and $\mathrm{PX}:\mathrm{XQ}=1:2.$ Calculate the lengths of $\mathrm{PR}$ and $\mathrm{QR}.$

In the figure, given below, $\mathrm{AB}, \mathrm{DC}$ and $\mathrm{EF}$ are parallel lines. Given $\mathrm{AB}=7.5\mathrm{cm}$, $\mathrm{DC}=y \mathrm{cm}$, $\mathrm{EF}=4.5\mathrm{cm}$, $\mathrm{BC}= x \mathrm{cm}$  and $\mathrm{CE}=3\mathrm{cm},$ Calculate the values of $x$ and $y\mathit{.}$