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    Theorem: If a, b, and c are numbers for which the sum of any two of them is greater than the third, then there is a triangle whose sides are of length a, b, and c.

    Explain the following proof: Assume that a â?¥ b and a â?¥ c. Draw a line segment of length a. At one end draw a circle of radius b. At the other end draw a circle of radius c. Join a point of intersection of these two circles with the end points of the line segment, as shown:

    What needs explanation is why the two circles must intersect. Please be detailed in your response.

    Why are the following two situations impossible? Please provide an explanation of your solution and/or reasoning.

    *********** see pdf attachment *************

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    Please see attached for the solution to the following problems.

    Hope this helps you in your studies.

    (see attached file for the diagram)

    Explanation:
    The two circles must intersect so that a triangle is formed. By connecting the two radii b and c on the intersecting point, a triangle is formed. The formation of triangle on the intersecting circles and joined radii only happens because the sum of lengths b and c is greater than a. The circles will not intersect if the sum of b and c is less than a.

    (see attached file for the diagram)

    Explanation: The first drawing shows that the length a is greater than the lengths b and c, as b is very small to create a circle that will intersect the larger one. Because of this, no triangle is formed. Similarly, in the second drawing, the two circles did not intersect because length c is much larger than the sum of a and b (as shown in the drawing, c is much larger than a alone). Because of this, no triangle is formed.

    The two problems prove the theorem that if a, b and c are numbers for which the sum of the two is greater than the third one, a triangle with sides a, b and c are formed.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 9:48 pm ad1c9bdddf>
    https://brainmass.com/math/triangles/applying-geometric-theorem-413776

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