H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Similar Triangles, Exercise 2: EXERCISE

In the figure below, if $DE\parallel BC$ and $AD=4x-3$, $AE=8x-7$, $BD=3x-1$ and $CE=5x-3$, find $x$.

In figure, if $AB\parallel CD$, find the value of $x$.

In the figure below, $PA, QB, RC$ and $SD$ are all perpendicular to a line $l$, $AB=6 \mathrm{cm}$, $BC=9 \mathrm{cm}$, $CD=12 \mathrm{cm}$ and $SP=36 \mathrm{cm}$. Find $PQ, QR$ and $RS$.

If $D$ and $E$ are respectively, the points on the sides $AB$ and $AC$ of a trianngle $ABC$, such that $AD=6 \mathrm{cm}$, $BD=9 \mathrm{cm}$, $AE=8 \mathrm{cm}$ and $EC=12 \mathrm{cm}$, then show that $DE\parallel BC$.

In $△ABC$, $\angle B=\angle C$, $D$ and $E$ are points on the sides $AB$ and $AC$ respectively, such that $BD=EC$. Prove that $DE\parallel BC$.

In $△ABC$, $D$ and $E$ are points on the sides $AB$ and $AC$ respectively, such that $AD\times EC=AE\times DB$. Prove that $DE\parallel BC$.

$ABCD$ is a parallelogram, $P$ is a point on side  $BC$. $DP$ when produced meets $AB$ produced to $L$, prove that $\frac{DP}{PL}=\frac{DC}{BL}$

$ABCD$ is a parallelogram, $P$ is a point on side  $BC$. $DP$ when produced meets $AB$ produced to $L$, prove that $\frac{DL}{DP}=\frac{AL}{DC}$