Sss geometry example tricia cole9/9/2023 ![]() Using four types of SSSs (βαβ-unit, α-hairpin, β-hairpin, αα-corner), we showed that extensive SSS sets could be reliably selected from the Protein Data Bank and AlphaFold 2.0 database of protein structures.ĪlphaFold 2.0 data bank graph neural network machine learning protein features super-secondary structure. For various types of SSS segmentation, this method uses key characteristics of SSS geometry, including the lengths of secondary structural elements and the distances between them, torsion angles, spatial positions of Cα atoms, and primary sequences. Here, we propose a universal PSSNet machine-learning method for SSS recognition and segmentation. Understanding known types of SSSs is important for developing a deeper understanding of the mechanisms of protein folding. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Thus, the two triangles (∆ABC and ∆DEF) are congruent by the SAS criterion.A super-secondary structure (SSS) is a spatially unique ensemble of secondary structural elements that determine the three-dimensional shape of a protein and its function, rendering SSSs attractive as folding cores. Solution for b): Step 1: a e gives the S. Note that you cannot compare donkeys with triangles Answer for a): a e, x u, c f is not sufficient for the above triangles to be congruent. This is not SAS but ASS which is not one of the rules. This means that our original assumption of assuming that ∠B ≠ ∠E is flawed: ∠B must be equal to ∠E. Step 2: Beware x and u are not the included angles. On the same segment, we cannot have two perpendiculars going in different directions. Example 4 Write a two-column proof to show that the two triangles are congruent. Line up the sides with the same number of tic marks. Don’t forget ORDER MATTERS when writing congruence statements. Lining up the corresponding sides, we have A B C L M K. To put it even more simply, note that BX and AX should both be perpendicular to GC (why?). From the SSS Postulate, the triangles are congruent. Is this possible? Can we have two isosceles triangles on the same base where the perpendiculars to the base are in different directions? No! What we have here is two isosceles triangles standing on the same base GC, where the perpendiculars from the vertex to the base (BX and AX) are in different directions. ![]() Similarly, since AG = AC, ∆AGC is isosceles. Now, take a good look at the following figure, in which we have highlighted to conclusions we just made (we have also marked X, the mid-point of GC): Thus, BG = BC.ĪG = DF, which is equal to AC. This leads to the following conclusions:īG = EF, which is equal to BC. Now, observe that ∆ABG will be congruent to ∆DEF, by the SAS criteria. Through B, draw BG such that ∠ABG = ∠DEF, and BG = EF, as shown below, and join A to G. One of the two angles must then be less than the other. ![]() Therefore, we begin our proof by supposing that none of the corresponding angles are equal. If we could show equality between even one pair of angles (say, ∠B = ∠E), then our proof would be complete, since the triangles would then be congruent by the SAS criterion. ![]() Consider two triangles once again, ∆ABC and ∆DEF, with the same set of lengths, as shown below: Let’s discuss the proof of the SSS criterion. ![]()
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