for this reason for any type of triangle, you deserve to divide the into four congruent triangles by connecting the midpoints of each side. Yet I desire to see just how this works.

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How walk SR can be proved to be same to AQ? SQ equal to RC? RQ equal to AS?


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$S$ is the midpoint that $AB$, so $|AS| = |SB| = \frac2$. Likewise for $R$, $|BR| = |RC| = \frac2$. Also, $\angle alphabet = \angle SBR$, therefore by SSA similarity $\triangle BSR \sim \triangle ABC$. The typical ratio is $1:2$, therefore $|SR| = \frac2 = |AQ| = |QC|$. The same goes because that $\triangle CQR$ and $\triangle ASQ$.

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