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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 10.4, Problem 15E
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Elementary Geometry for College St...

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

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
BuyFindarrow_forward

Elementary Geometry for College St...

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

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

If the midpoint of one side of a rectangle is joined to the endpoints of the opposite side, then an isosceles triangle is formed.

To determine

To answer:

The analytic proof for the given theorem “If the midpoint of one side of a rectangle is joined to the endpoints of the opposite side, then an isosceles triangle is formed”.

Explanation

Given theorem is,

If the midpoint of one side of a rectangle is joined to the endpoints of the opposite side, then an isosceles triangle is formed.

The above figure shows the rectangle ABCD.

The vertices of the rectangle ABCD is A (0, 0), B (2a,0) and C (2a,2b), D (0, 2b).

And M is the midpoint of the side CD.

Joining the midpoint M to the end of the opposite side A and B as shown in above figure and is forming the triangle ABM.

Based on the midpoint formula,

The midpoint of CD =M=2a+02,2b+2b2

The midpoint of CD =M=2a2,4b2

The midpoint of CD =M=a,2b

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

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

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