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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 1 to 17, complete an analytic proof for each theorem.

The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle.

To determine

To answer:

The analytic proof for the given theorem “The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle”.

Explanation

Given theorem is,

The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle.

The above figure shows the right triangle ABC.

The vertices of the triangle ABC is A (2a,0), B (0, 2b) and C (0, 0).

AB is the hypotenuse of the right triangle.

And D is the midpoint of the hypotenuse AB.

Hence, AD=BD.

Based on the midpoint formula,

The midpoint of AB =D=0+2a2,2b+02

The midpoint of AB =D=a,b

Based on the distance formula, the length of AD as below,

AD =(2a-a)2-(0-b)2

AD =(a)2-(-b)2

AD =(a

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