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Study Triangle Similarity and study Supplementary Angles, from the standard high school Geometry course. The triangle problem with the single square relies on supplementary angles where the upper right and left square vertices meet two sides of the larger triangle. You can conclude that all three of the smaller triangles are similar, and so the ratios of their corresponding sides are equal. A proportion can be arranged for the two smaller left & right-hand triangles; and note too that all three of the smaller triangles are RIGHT triangles.
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