Amrit shows that triangle QTS is congruent to triangle SRQ by rotating triangle QTS 180° around point C so it matches up with triangle SRQ 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 answer is: If two pairs of angles and the included side are congruent, the triangles are congruent.
Explanation: When triangle QTS is rotated to match triangle SRQ, the congruence of the two triangles can be established if at least two pairs of corresponding angles are equal and the included side between those angles is also equal. This is known as the Angle-Angle-Side (AAS) theorem which asserts that if two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, then the triangles are congruent.