Answered: Suppose that the side lengths of one of…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Suppose that the side lengths of one of a pair of 5-con trianglesare given by the numbers (a, b, c), where a<b<c. Suppose the other triangle in the 5-con pair is a scaled version of the first triangles by a factor of k, where k>1. (That is, the side lengths of the second triangle are (ka, kb, kc).) Prove that the side lengths ofthe original triangle must be of the form (a, ak, ak2), that is the side lengths must be triples from a geometric sequence.

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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