Question - Congruent Triangles and Side Lengths
Solution:
The image shows a pair of congruent triangles, ΔDEG and ΔEFG, with DE congruent to EF, DG equal to 3a, and FG equal to a + 42. In congruent triangles, corresponding sides are equal in length. Therefore:DE = EFSince FG is the sum of DG and EG, and EG is equal to DE (because DE = EF and EF = EG by congruency), you can express FG as:FG = DG + EGGiven:DG = 3aEG = DE = EF (Because of the congruency between ΔDEG and ΔEFG)Since DE is congruent to EF, that implies EG = EF. So using the information that FG = DG + EG, we can substitute the given values into the equation:FG = 3a + EFWe were also given that FG = a + 42. This allows us to set up the following equation since they both represent FG:3a + EF = a + 42However, to find FG, we do not actually need to solve for a or EF individually since FG equals a + 42 by the given information. Therefore:FG = a + 42This is the expression for FG, and without additional information or numerical values provided for a, this is as simplified as it gets.
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