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Name: Prove the following both indirectly in paragraph form and also in a tw
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Description: Prove the following both indirectly in paragraph form and also in a two column formal proof format: Prove that the sum of the lengths of the medians of a triangle is greater than half the perimeter.

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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Prove the following both indirectly in paragraph form and also in a two column formal proof format: Prove that the sum of the lengths of the medians of a triangle is greater than half the perimeter.

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°).

Expert Solution

Step 1

Let ABC be a triangle with sides AB, BC, and CA. Also, M is the mid-point of AB and m_c is the median coming from C. Figure is given below

Step 2

Formula Used:

The sum of ant two sides of a triangle is greater than the median drawn to the third side.
If a, b, and c are the sides of a triangle then the parameter of the triangle is a + b + c.

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