Triangular proof, math homework help

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timer Asked: Jun 17th, 2016
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Question description

Consider the theorems below:

The following is a theorem of Euclidean geometry:
Euclidean angle sum theorem: The sum of the measures of the angles of a triangle is 180°.

Theorem 1: An exterior angle of a triangle is greater than either of the nonadjacent interior angles of the triangle.
 

A. Using the Euclidean angle sum theorem, prove Theorem 1. Your proof must refer to the definitions provided below.

Definitions:

•  adjacent: Two angles are adjacent if they share a common vertex and common side, and they do not overlap. Otherwise, the two angles are nonadjacent.

•  supplementary:Two angles are supplementary if their measures sum to 180°.

•  exterior:An angle that is both adjacent and supplementary to an angle of a triangle is an exterior angle of the triangle.

1. Explain why this theorem is also true in hyperbolic geometry.

2. Explain why this theorem is not true in spherical geometry.


COLLEGE GEOMETRY Competency 218.1.1: Axiomatic Systems - The graduate applies the axiomatic nature of geometry to analyze the fundamental concepts and principles of Euclidean and nonEuclidean geometries. Competency 218.1.2: Properties and Relationships - The graduate applies synthetic and analytic methods to construct proofs and solves problems involving the properties and relationships of two-dimensional objects. Task 2: Euclidean Proof Introduction: In this task, you will prove one statement regarding fundamental concepts and principles of geometry. Your proof may use only the given theorems and definitions. Requirements: Your submission must be your original work. No more than a combined total of 30% of the submission and no more than a 10% match to any one individual source can be directly quoted or closely paraphrased from sources, even if cited correctly. Use the Turnitin Originality Report available in Taskstream as a guide for this measure of originality. You must use the rubric to direct the creation of your submission because it provides detailed criteria that will be used to evaluate your work. Each requirement below may be evaluated by more than one rubric aspect. The rubric aspect titles may contain hyperlinks to relevant portions of the course. Consider the theorems below: The following is a theorem of Euclidean geometry: Euclidean angle sum theorem: The sum of the measures of the angles of a triangle is 180°. Theorem 1: An exterior angle of a triangle is greater than either of the nonadjacent interior angles of the triangle. A. Using the Euclidean angle sum theorem, prove Theorem 1. Your proof must refer to the definitions provided below. Definitions: • adjacent: Two angles are adjacent if they share a common vertex and common side, and they do not overlap. Otherwise, the two angles are nonadjacent. • supplementary:Two angles are supplementary if their measures sum to 180°. • exterior:An angle that is both adjacent and supplementary to an angle of a triangle is an exterior angle of the triangle. 1. Explain why this theorem is also true in hyperbolic geometry. 2. Explain why this theorem is not true in spherical geometry. B. Acknowledge sources, using in-text citations and references, for content that is quoted, paraphrased, or summarized.

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tutorjohn
School: Rice University

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Anonymous
Good stuff. Would use again.

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