Question

Select the correct answer from each drop-down menu. Two triangles ABC and GEF are represented. Segment AC and segment EG have a single tick mark. Segment BC and segment GF have double tick marks. The condition proves that ΔABC and ΔEFG are congruent by the SAS criterion. If AB ≠ EF, the criterion for congruency is violated. In this situation, angle C ______ angle G?

1) is equal to
2) is not equal to
3) cannot be determined

Answer 1

Without knowing if the angles between the congruent sides are also equal, we cannot state if angle C is equal to angle G; thus, the correct answer is that it cannot be determined based on the given information.

Step-by-step explanation:

The condition that proves triangles ABC and EFG are congruent by the SAS criterion is that two sides and the angle between them must be equal in both triangles. Given that segment AC and segment EG have single tick marks, and segment BC and segment GF have double tick marks, we can infer that these sides are equal. However, if side AB is not equal to side EF, then the triangles will not meet the SAS criterion for congruency. Therefore, in this case, we cannot determine if angle C is equal to angle G without additional information about the angles. The congruence of angles C and G is not implied solely by the side lengths, thus the correct answer to the question 'In this situation, angle C cannot be determined to be equal or not equal to angle G'.