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

Question
Similarity asked 2021-02-02
Proving Similarity in the figure DEFG is a square. Prove the following:
$$\displaystyle\triangle{A}{D}{G}\sim\triangle{G}{C}{F}$$
Given:
The given figure is, ## Answers (1) 2021-02-03
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 $$\displaystyle{180}^{{\circ}}$$. Therefore, the triangles are similar by AA rule if two angles are same.
Calculation:
It is given that DEFG is a square.
Consider $$\displaystyle\triangle{A}{D}{G}{\quad\text{and}\quad}\triangle{G}{C}{F}$$.
$$\displaystyle\angle{A}{D}{G}=\angle{G}{C}{F}$$ both are $$\displaystyle{90}^{{\circ}}$$.
And $$\displaystyle{G}{F}{\mid}{\mid}{A}{B}$$, thus, $$\displaystyle\angle{C}{G}{F}=\angle{G}{A}{D}$$ as they are alternate angles.
Therefore, $$\displaystyle\triangle{A}{D}{G}\sim\triangle{G}{C}{F}$$ by AA rule.
Conclusion:
Hence, it is proved that $$\displaystyle\triangle{A}{D}{G}\sim\triangle{G}{C}{F}$$.

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