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

FizeauV 2021-02-02 Answered

Proving Similarity in the figure DEFG is a square. Prove the following:
$\mathrm{△}ADG\sim \mathrm{△}GCF$
Given:
The given figure is,

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## Expert Answer

Maciej Morrow
Answered 2021-02-03 Author has 98 answers
Approach:
Two triangles are similar if their vertices can be matched up so that corresponding angles are congruent. In this case corresponding sides are proportional.
If the two angles of the triangles are same then the third angle of the triangles have to be same,because the sum of angles in a triangle is ${180}^{\circ }$. Therefore, the triangles are similar by AA rule if two angles are same.
Calculation:
It is given that DEFG is a square.
Consider $\mathrm{△}ADG\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\mathrm{△}GCF$.
$\mathrm{\angle }ADG=\mathrm{\angle }GCF$ both are ${90}^{\circ }$.
And $GF\mid \mid AB$, thus, $\mathrm{\angle }CGF=\mathrm{\angle }GAD$ as they are alternate angles.
Therefore, $\mathrm{△}ADG\sim \mathrm{△}GCF$ by AA rule.
Conclusion:
Hence, it is proved that $\mathrm{△}ADG\sim \mathrm{△}GCF$.
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