To prove that triangle cap d cap f cap e approximates triangle cap g cap f cap h by the SAS similarity theorem, it can be stated that the fraction with numerator cap d cap f and denominator cap g cap f is equal to the fraction with numerator cap e cap f and denominator cap h cap f and

For SAS similarity, the angles between the two pairs of proportional sides must be congruent. In triangle DFE, the sides DF and EF meet at F, forming angle DFE. In triangle GFH, the sides GF and HF meet at F, forming angle GFH. Therefore, angle DFE must be congruent to angle GFH.

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