Question

The condition_________? proves that ∆ABC and ∆EFG are congruent by the SAS criterion. A. Angle A is congruent to angle E B. B is congruent to angle F C. AB=EF D. Angle C is congruent to angle G

Answer 1

The condition AB = EF proves that ∆ABC and ∆EFG are congruent by the SAS criterion.

Step-by-step explanation:

The condition AB = EF proves that ∆ABC and ∆EFG are congruent by the SAS criterion.

SAS stands for Side-Angle-Side, which means that if two sides of one triangle are congruent to two sides of another triangle and the included angle between those sides is congruent, then the triangles are congruent. In this case, AB is congruent to EF, and since this condition satisfies the SAS criterion, ∆ABC and ∆EFG are congruent.

Answer 2

The condition AB = EF proves that ∆ABC and ∆EFG are congruent by the SAS criterion.

Step-by-step explanation:

The Side-Angle-Side (SAS) criterion states that if two triangles have two sides and the included angle equal, then the triangles are congruent. In this case, we are given that AB = EF. This fulfills the side requirement. Now, let's understand why the angle condition is met.

To establish the SAS criterion, we need to identify the corresponding angles between the triangles. In this scenario, we need to ensure that the included angle between the equal sides in both triangles is congruent. However, the question doesn't explicitly provide information about the included angles (e.g., angles at B and F). Therefore, we need to consider the congruence of angles indirectly.

Since the question doesn't state the specific angles, we assume that angle A corresponds to angle E, angle B corresponds to angle F, and angle C corresponds to angle G. The side AB = EF implies that angle A is congruent to angle E (by the Angle-Side property). Thus, the condition AB = EF, combined with the assumed congruence of angles A and E, establishes the SAS criterion and proves that ∆ABC and ∆EFG are congruent.