In the figure, ABC is an isosceles triangle, right-angled at C. Therefore:

It is given that $\mathrm{△}ABC\backslash triangle\; ABC$ $\sim \backslash sim$ $\mathrm{△}PQR,\backslash triangle\; PQR,$ with $\frac{BC}{QR}=\frac{1}{4}\mathrm{.}\backslash frac\{BC\}\{QR\}=\backslash frac14.$ Then, $\frac{ar\mathrm{\Delta }PQR}{ar\mathrm{\Delta }ABC}\backslash frac\{ar\backslash Delta\; PQR\}\{ar\backslash Delta\; ABC\}$ is equal to:

If in two triangles $\mathrm{△}DEF\backslash triangle\; DEF$ and $\mathrm{△}PQR,\backslash triangle\; PQR,$ $\mathrm{\angle }D=\mathrm{\angle }Q\backslash angle\; D=\backslash angle\; Q$ $and\mathrm{\angle }R=\mathrm{\angle }E,and\backslash ;\backslash angle\; R=\backslash angle\; E,$ then which of the following is not true?

Let $\mathrm{△}ABC\sim \mathrm{△}DEF\backslash triangle\; ABC\backslash sim\backslash triangle\; DEF$ and their areas be $81c{m}^{2}and144c{m}^2\mathrm{.}81\backslash ,cm^2\backslash ;and\backslash ;144\backslash ,cm^2.$ If EF = 24 cm, then length of side BC is ........ cm.

In figure, $\mathrm{\angle }BAC={90}^{\circ }\backslash angle\; BAC=90^\backslash circ$ and AD $\mathrm{\perp }\backslash bot$ BC. Then,

The length of each side of a rhombus whose diagonals are of lengths 10 cm and 24 cm is

If $\mathrm{△}ABC\sim \mathrm{△}EDF\backslash triangle\; ABC\backslash sim\backslash triangle\; EDF$ and $\mathrm{△}ABC\backslash triangle\; ABC$ is not similar to $\mathrm{△}DEF,\backslash triangle\; DEF,$ then which of the following is not true?

If $\mathrm{△}ABC\sim \mathrm{△}DEF,\backslash triangle\; ABC\backslash sim\backslash triangle\; DEF,$ $\frac{ar(\mathrm{△}ABC)}{ar(\mathrm{△}DEF)}=\frac{9}{25},\backslash frac\{ar(\backslash triangle\; ABC)\}\{ar(\backslash triangle\; DEF)\}=\backslash frac9\{25\},$ BC = 21 cm, then EF is equal to

D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 3 cm, BD = 5 cm, BC = 12.8 cm and DE || BC. Then length of DE (in cm) is

If in two triangles ABC and PQR, $\frac{AB}{QR}=\frac{BC}{PR}=\frac{CA}{PQ},\backslash frac\{AB\}\{QR\}=\backslash frac\{BC\}\{PR\}=\backslash frac\{CA\}\{PQ\},$ then

If $\mathrm{\Delta }PRQ\sim \mathrm{\Delta }XYZ,\backslash Delta\; PRQ\backslash sim\backslash Delta\; XYZ,$ then

A square and a rhombus are always

In triangles ABC and DEF, $\mathrm{\angle }B=\mathrm{\angle }E,\mathrm{\angle }F=\mathrm{\angle }C\backslash angle\; B=\backslash angle\; E,\backslash angle\; F=\backslash angle\; C$ and AB = 3DE. Then the two triangles are

It is given that $\mathrm{\Delta }\backslash Delta$ABC $\sim \backslash sim$ $\mathrm{\Delta }\backslash Delta$DFE, $\mathrm{\angle }A={30}^{\circ },\mathrm{\angle }C={50}^{\circ },\backslash angle\; A=30^\backslash circ,\backslash angle\; C=50^\backslash circ,$ AB = 5 cm, AC = 8 cm and DF = 7.5 cm. Then, which of the following is true?

Two circles are always