Question

select the correct answer from each drop - down menu.
the condition proves that \\( \triangle abc \\) congruent by the sas criterion.
if \\( ab\
eq ef \\), the criterion for congruency is violated. in this situation, angle \\( c \\) angle \\( g \\).

Explanation:

• For the first part, in the SAS (Side - Angle - Side) criterion, we need two sides and the included angle to be equal. If \(BC = FG\), \(AB = EG\) (assuming from the figure's markings), and \(\angle ABC=\angle EGF\) (the included angles), then \(\triangle ABC\cong\triangle EGF\) by SAS.
• For the second part, SSA (Side - Side - Angle) is not a valid congruence criterion in general (except for right - angled triangles where it is equivalent to HL). If \(AB

eq EF\), the SSA criterion (which was wrongly assumed if we thought of non - included angle and two sides) is violated.

• For the third part, just because the SSA criterion is violated does not mean the angles \(\angle C\) and \(\angle G\) are not equal. Congruence is a stronger condition than just having some angles equal. There is no information to suggest that \(\angle C\) and \(\angle G\) are not equal.

Answer:

1. \(BC = FG\) (assuming from the figure's markings for the SAS condition)
2. SSA
3. is not necessarily not equal to