Triangle inequality homework

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Students can connect algebra to geometry by expressing geometric inequalities in compound inequality form. Since the sum of the lengths of any two sides of a triangle is greater than the length of the third side, there are three inequality statements. All three inequality statements must be true for three line segments to form a triangle. The perimeter of any polygon is the sum of the measurements of its sides. Therefore, the perimeter of a triangle is the sum of the measurements of its three sides. Suppose a triangle has 3 sides with measurements a, b, and c.
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Triangle inequality?

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Triangle Inequality & Angle-Side Relationship (solutions, examples, videos)

Use an inequality to prove your answer. A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question Q: A cube with sides n cm long is painted on all faces.
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Geometry: Triangle Inequality and Angle-Side Relationship

In mathematics , the triangle inequality states that for any triangle , the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side. In Euclidean geometry and some other geometries, the triangle inequality is a theorem about distances, and it is written using vectors and vector lengths norms :. In Euclidean geometry, for right triangles the triangle inequality is a consequence of the Pythagorean theorem , and for general triangles, a consequence of the law of cosines , although it may be proven without these theorems. The figure at the right shows three examples beginning with clear inequality top and approaching equality bottom. Thus, in Euclidean geometry, the shortest distance between two points is a straight line.
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