Proving Similarity in the figure DEFG is a square. Prove the following:/_ADG~/_FEBGiven:The given figure is,12210202691.jpg

Approach:
If the first triangle is similar to the second triangle and second triangle is similar to the third triangle then, the first triangle is similar to the third triangle.
Calculation:
Its given that DEFG is a square.
Consider ${\displaystyle \mathrm{△}GCF\text{and}\mathrm{△}FEB}$.
${\displaystyle \mathrm{\angle }FEB=\mathrm{\angle }GCF}$ both are ${\displaystyle {90}^{\circ }}$.
And ${\displaystyle GF\mid \mid AB,thus,\mathrm{\angle }CFG=\mathrm{\angle }FBE}$ as they are alternate angles.
Therefore, ${\displaystyle \mathrm{△}GCF\sim \mathrm{△}FEB}$ by AA rule.
Since, ${\displaystyle \mathrm{△}GCF\sim \mathrm{△}FEB\text{and}\mathrm{△}ADG\sim \mathrm{△}GCF,hence,\mathrm{△}ADG\sim \mathrm{△}FEB}$
Conclusion:
Hence, it is proved that ${\displaystyle \mathrm{△}ADG\sim \mathrm{△}FEB}$.