Jake shows that ΔCBA is congruent to ΔADC by rotating ΔCBA 180° around point C so it matches up with ΔADC exactly. Which conclusion can be drawn from Jake’s transformations?
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.
If two pairs of angles and the included side are congruent, the triangles are congruent.
If one pair of angles is congruent, then all pairs of angles are congruent.
The correct conclusion that can be drawn from Jake’s transformations is:
If two pairs of angles and the included side are congruent, the triangles are congruent.
Explanation: Since Jake showed that ΔCBA is congruent to ΔADC by rotating the triangle, it indicates that all corresponding angles and sides are equal, which means the triangles are congruent by the Angle-Side-Angle (ASA) postulate. This postulate establishes that if two angles and the included side of one triangle are equal to the corresponding parts of another triangle, then the triangles are congruent.
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