Question

question 9
1 pts
suppose △abc≅△efg. which congruency statement is true?
○ (overline{ac}congoverline{ef})
○ (overline{ab}congoverline{eg})
○ (overline{bc}congoverline{fg})
○ (overline{ab}congoverline{fg})

Explanation:

Step1: Recall congruent - triangle property

When \(\triangle ABC\cong\triangle EFG\), corresponding sides are congruent. That is, \(AB\) corresponds to \(EF\), \(BC\) corresponds to \(FG\), and \(AC\) corresponds to \(EG\).

Step2: Analyze each option

• Option 1: \(AC\) corresponds to \(EG\), not \(EF\), so \(\overline{AC}\cong\overline{EF}\) is false.
• Option 2: \(AB\) corresponds to \(EF\), not \(EG\), so \(\overline{AB}\cong\overline{EG}\) is false.
• Option 3: Since \(BC\) corresponds to \(FG\) in \(\triangle ABC\cong\triangle EFG\), \(\overline{BC}\cong\overline{FG}\) is true.
• Option 4: \(AB\) corresponds to \(EF\), not \(FG\), so \(\overline{AB}\cong\overline{FG}\) is false.

Answer:

\(\overline{BC}\cong\overline{FG}\)