Chapter 4.4, Problem 34E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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.

M and N are the midpoints of ADÂ¯â€Šâ€Šandâ€ŠBCÂ¯.

P and Q are the midpoints of ABÂ¯â€Šâ€Šandâ€ŠDCÂ¯.

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

It means âˆ ABDâ‰…âˆ BDC.

Therefore, Î”ABDâ€Šâ€Šâ‰…â€Šâ€ŠÎ”CBD 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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