To find: the length of MN¯

Expert Solution & Answer

Answer to Problem 17CUR

MN=3r−s

Explanation of Solution

Given:

M and N are the midpoints of the legs of the trapezoid EFGH .

EF¯=2r+s

HG¯=4r−3s

Consider the figure shown below representing the given question:

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 5, Problem 17CUR

Consider the trapezoid EFGH .

M and N are the midpoints of the legs of the trapezoid EFGH . So, MN¯ is the median of the trapezoid EFGH .

So, by theorem 5-19 part (2), the length of the median MN¯ is equal to the average of the base lengths EF¯ and HG¯ .

Thus,

MN=12(MN+HG)=12(2r+s+4r−3s)=12(6r−2s)=3r−s

Chapter 5, Problem 16CUR

Chapter 5, Problem 18CUR

Chapter 5 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

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