Question

complete the proof that (overleftrightarrow{ab} parallel overleftrightarrow{cg}).
step statement rea
1 (cf = ae) bot
hav
the
leng
2 (cg = ad) bot
hav
the
leng
3 bot
hav
the
leng

• (fg = ae)
• (fg = ad)
• (fg = ed)

4 (\triangle cgf) side
con
2, 3

Explanation:

Step1: Analyze the proof context

We are proving \( \overleftrightarrow{AB} \parallel \overleftrightarrow{CG} \), likely using congruent triangles or parallel line criteria. The first two steps give \( CF = AE \) and \( CG = AD \), and we need to find the correct statement for step 3.

Step2: Evaluate the options

• Option "FG = AE": If we consider the diagram (assuming a grid or equal - length segments, maybe related to the "bottom" having equal lengths as per the reason "Botl hav the leng" (likely "Bottoms have the length")), this could be consistent with the other equal - length statements (\( CF = AE \), \( CG = AD \)) to build up congruent triangles (e.g., for \( \triangle CGF \) and another triangle).
• Option "FG = AD": There's no prior indication that \( FG \) should equal \( AD \) from the first two steps.
• Option "FG = ED": There's no prior relation given between \( FG \) and \( ED \) to suggest this equality. So the most consistent option is \( FG = AE \).

Answer:

FG = AE