Amrit shows that ΔQTS is congruent to ΔSRQ by rotating ΔQTS 180° around point C so it matches up with ΔSRQ exactly. Which conclusion can be drawn from Amrit’s transformations?
If one pair of angles is congruent, then all pairs of angles are congruent.
If two pairs of angles and the included side are congruent, the triangles are congruent.
If the triangles share one side, the triangles are congruent.
If two triangles are congruent, a dilation can be used to match them up exactly.
The correct conclusion that can be drawn from Amrit’s transformations is:
If two pairs of angles and the included side are congruent, the triangles are congruent.
Explanation: Since Amrit successfully rotated triangle ΔQTS by 180° around point C to coincide exactly with triangle ΔSRQ, this indicates that the corresponding sides and angles of both triangles are congruent. In triangle congruence, one common case is the Angle-Side-Angle (ASA) criterion, which states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. This rotation verifies that all corresponding parts of the triangles are congruent, supporting this conclusion.