   Chapter 4.4, Problem 34E 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 29 to 35, complete a formal proof.If the midpoints of the sides of an isosceles trapezoid are joined in order, then the quadrilateral formed is a rhombus.

To determine

To Prove:

If the midpoints of the sides of an isosceles trapezoid are joined in order, then the quadrilateral formed is a rhombus.

Explanation

Consider the following trapezoids ABCD.

For an isosceles trapezoid AB||DCandADBC.

M and N are the midpoints of AD¯andBC¯.

P and Q are the midpoints of AB¯andDC¯.

If two parallel lines are cut by a transversal alternate interior angles are congruent.

It means ABDBDC.

Therefore, ΔABDΔCBD by SAS (If two sides and included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent)

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