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

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

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

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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