If we could show that KL = c, then we can tie together the following pairs of segments
EG = KM = a
GF = ML = b
EF = KL = c
Then we'd use the SSS congruence theorem to prove the triangles are congruent. The last step is to use CPCTC to conclude that angle EGF is a 90 degree angle.
Keep in mind that we need to know the actual numeric values of 'a' and 'b' to be able to determine the value for c. So without the numbers, the Pythagorean theorem isn't really useful; however, I can see where your teacher is going with this line of logic. Your teacher is effectively just laying out a basic outline more or less.
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Notes:
SSS = side side side
CPCTC = corresponding parts of congruent triangles are congruent
The answer is Option C) 7th graders in her school.
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