   Chapter 10.4, Problem 19E 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

Use the analytic method to decide what type of triangle is formed when the midpoints of the sides of an isosceles triangle are joined by line segments.

To determine

What type of triangle is formed for the given condition?

Explanation

Given theorem is,

The midpoints of the sides of an isosceles triangle are joined by line segments

The above figure shows the isosceles triangle ABC.

E, F and G are the midpoints of the ides of the isosceles triangle AB, BC and AC respectively.

Now, joining the midpoints EF, FG and GE as shown in the above figure.

The coordinate of the quadrilateral ABCD is A0, 0, B2a, 0 and C(a,b)

The midpoint of AB =E=0+2a2,0+02

The midpoint of AB =E=2a2,0

The midpoint of AB =E=a,0

The midpoint of BC =F=2a+a2,0+b2

The midpoint of BC =F=3a2,b2

The midpoint of AC =G=a+02,b+02

The midpoint of AC =G=a2,b2

Using distance formula,

EF =3a2

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