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Chapter 5: Problem 58

Determine whether the statement is true or false. Justify your answer. Two angles and one side of a triangle do not necessarily determine a unique triangle.

Short Answer

Expert verified
The given statement is false. According to the Angle-Angle-Side (AAS) Congruence theorem in geometry, two angles and one side of a triangle do determine a unique triangle.

Step by step solution

01

Concept Understanding

The first thing to grasp is the concept of Angle-Angle-Side (AAS) Congruence in triangles. If two angles and one side (the side doesn't have to be between the two angles) are the same in two different triangles, then the triangles are congruent by the AAS theorem.
02

Evaluation of the Statement

Based on the concept understood from Step 1, evaluate the given statement: 'Two angles and one side of a triangle do not necessarily determine a unique triangle.' Since two angles and one side of a triangle necessarily determine a unique triangle according to AAS Congruence, the given statement can be concluded as false.
03

Justification

Justify the result based on AAS Congruence theorem. Since it has been established that two angles and one side of a triangle do determine a unique triangle, the statement in the exercise is false. Therefore, with an understanding of the AAS theorem, the false statement can be justified.

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