Question

Triangle ADB and Triangle BFC, congruent? Which postulate did you use for your proof? Which engineer was correct?

A) The triangles are congruent by SAS (Side-Angle-Side), and Engineer 1 was correct.
B) The triangles are congruent by ASA (Angle-Side-Angle), and Engineer 2 was correct.
C) The triangles are congruent by SSS (Side-Side-Side), and both engineers were correct.
D) The triangles are not congruent, and neither engineer was correct.

Answer 1

The triangles ADB and BFC are congruent by the ASA (Angle-Side-Angle) postulate, and Engineer 2 was correct.

Step-by-step explanation:

To determine the congruence of triangles ADB and BFC, we compare the corresponding angles and sides between the two triangles. From the given information, angle ADB is congruent to angle BFC (both are right angles), angle DAB is congruent to angle FCB (given), and side AB is congruent to itself (common side). Thus, we have two pairs of congruent angles and one pair of congruent sides, satisfying the conditions for the ASA postulate.

According to the ASA postulate, if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. In this case, triangles ADB and BFC meet this criteria, establishing their congruence by the ASA postulate.

Therefore, Engineer 2 was correct in stating that the triangles ADB and BFC are congruent by the ASA postulate. This method aligns with the provided information regarding the angles and sides of the triangles, proving their congruence based on the specified postulate.