Embibe Experts Solutions for Chapter: Geometry, Exercise 1: Similar triangles

$∆ABC$ and $∆DEF$ are similar. Also $\angle A=\angle D$ and $\angle B=\angle E$. If $4AB=DE$ and $BC=12$ $cm$, then $EF$ is equal to

In a $∆ABC$, the sides $AB$, $BC$ and $CA$ are $10$ $\mathrm{cm}$, $8$ $\mathrm{cm}$ and $7$ $\mathrm{cm}$. On $AB$ a point $P$ is taken such that $AP=4$ $\mathrm{cm}$. If $PQ$ is drawn parallel to $BC$, then its length is equal to:

One-fifth of the area of a triangle $ABC$ is cut off by a line $DE$ drawn parallel to $BC$ such that$D$ is on $AB$ and $E$ is on $AC$. If $BC=10 \mathrm{cm}$, then what is $DE$ equal to?

The diagonals of a cyclic quadrilateral $ABCD$ intersect at $P$ and the area of the triangle $APB$ is $24 {\mathrm{cm}}^2$. If $AB=8 \mathrm{cm}$ and $CD=5 \mathrm{cm}$, then what is the area of the triangle $CPD$?

In $∆ABC$ the straight line parallel to the side $BC$ meets $AB$ and $AC$ at the points $P$ and $Q$ respectively. If $AP=QC$ the length of $AB$ is $12$ units and the length of $AQ$ is $2$ units then the length (in units) of $CQ$ is

$\mathrm{D}$ and $\mathrm{E}$ are points on side $\mathrm{AB}$ and $\mathrm{AC}$ of $∆\mathrm{ABC}$. $\mathrm{DE}$ is parallel to $\mathrm{BC}$. If $\mathrm{AD}:\mathrm{DB}=2 : 3$, What is the ratio of area of $∆\mathrm{ADE}$ and area of quadrilateral $\mathrm{BDEC}$ ?

The areas of two similar triangles $ABC$ and $DEF$ are $36 c{m}^2$ and $81 c{m}^2$, respectively. If $EF = 6.3 cm$, measure of $BC$ is:

If the three angles of a triangle are equal to the three angles of another triangle, then the triangles are always _____.