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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In Exercises 31 to 34, apply a form of Theorem 3.5.10.

Prove by the indirect method: “The length of a diagonal of a square is not equal in length to the length of any of the sides of the square.”

Chapter 3.5, Problem 34E, In Exercises 31 to 34, apply a form of Theorem 3.5.10. Prove by the indirect method: The length of a

To determine

To prove:

The length of a diagonal of a square is not equal in length to the length of any of the sides of the square.

Explanation

Given:

The square ABCD is shown in the below figure,

Figure (1)

Approach:

The length of any side of a triangle must lie between the sum and difference of the lengths of the other two sides.

Assume, the length of all the sides of the square is x and the length of the diagonal of the square is y.

Consider the triangle ΔABC,

The length of the two sides of the triangle ΔABC is x

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