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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Section
BuyFindarrow_forward

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

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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