Question

Answer each question. Eli Maor, a perceptive trigonometry student, makes this statement: "If we know any two angles and one side of a triangle, then the triangle is uniquely determined." Why is this true? Refer to the congruence axioms given in this section.

Name: Problem 31, Chapter 7: Trigonometry
Uploaded: 2023-03-10T03:44:04-08:00
Duration: 1 min 18 s
Channel: Aman Gupta
Description: Answer each question. Eli Maor, a perceptive trigonometry student, makes this statement: "If we know any two angles and one side of a triangle, then the triangle is uniquely determined." Why is this true? Refer to the congruence axioms given in this section.

   Answer each question.
Eli Maor, a perceptive trigonometry student, makes this statement: "If we know any two angles and one side of a triangle, then the triangle is uniquely determined." Why is this true? Refer to the congruence axioms given in this section.

Trigonometry

Margaret L. Lial,… 11th Edition

Chapter 7, Problem 31

Instant Answer

Solved by Expert Aman Gupta

03/10/2023

Step 1

These axioms state that if two triangles have congruent corresponding sides and angles, then the triangles are congruent. Now, let's apply this to the statement made by Eli Maor. If we know any two angles and one side of a triangle, we can use this information to Show more…

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Answer each question. Eli Maor, a perceptive trigonometry student, makes this statement: "If we know any two angles and one side of a triangle, then the triangle is uniquely determined." Why is this true? Refer to the congruence axioms given in this section.

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Key Concepts

Triangle Angle Sum Property

In any triangle, the sum of the interior angles is always 180°. This fundamental property allows us to calculate the third angle when two are known, ensuring that the triangle's shape is fully determined by its angles.

ASA and AAS Congruence Axioms

The ASA (Angle-Side-Angle) and AAS (Angle-Angle-Side) congruence axioms state that if two triangles have two pairs of corresponding angles equal and a corresponding side equal (between the angles in ASA or not necessarily adjacent in AAS), then the triangles are congruent. This congruence implies that the triangle is uniquely determined.

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