Question

given: \\(\frac{fe}{de} = \frac{ge}{ce}\\)
prove: \\(\triangle dec sim \triangle feg\\)

fill in the missing reason for the proof.

a corresponding angles
b sss similarity theorem
c vertical angles
d sss congruence theorem

Explanation:

To determine the missing reason, we analyze the angles ∠DEC and ∠FEG. These angles are formed by the intersection of lines DC and FG at point E, so they are vertical angles. Vertical angles are always congruent, which is the reason for ∠DEC ≅ ∠FEG. Option A (Corresponding Angles) is incorrect as these are not corresponding angles from parallel lines. Option B (SSS Similarity Theorem) and D (SSS Congruence Theorem) are irrelevant here as we are dealing with angles, not side - side - side relationships.

Answer:

C. Vertical Angles