Congruent Triangles and Side Lengths
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 = EF
Since 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 + EG
Given:
DG = 3a
EG = 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 + EF
We were also given that FG = a + 42. This allows us to set up the following equation since they both represent FG:
3a + EF = a + 42
However, 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 + 42
This is the expression for FG, and without additional information or numerical values provided for a, this is as simplified as it gets.
