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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 provided statement is false. According to the Angle-Side-Angle (ASA) postulate, having two angles and the included side equal to another triangle necessarily determines a unique triangle.

Step by step solution

01

Analyze the Statement

We need to consider the statement and understand what it means. According to the statement, two angles and one side of a triangle do not necessarily determine a unique triangle. Technically this means having the same measurement of two angles and one side could result in different triangles.
02

Consider the ASA Postulate

The Angle-Side-Angle (ASA) postulate states that if two angles and the side between them in one triangle is congruent to two angles and the included side in another triangle, the triangles are congruent. Congruent triangles are identical and unique.
03

Compare the Statement with the ASA postulate

The given statement that two angles and one side of a triangle do not necessarily determine a unique triangle, contradicts the ASA postulate.

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