McDougal Littell Jurgensen Geometry: Student Edition Geometry
McDougal Littell Jurgensen Geometry: Student Edition Geometry
5th Edition
ISBN: 9780395977279
Author: Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Publisher: Houghton Mifflin Company College Division
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Chapter 13.9, Problem 3WE
To determine

To prove: median of a trapezoid is parallel to its bases.

Expert Solution & Answer
Check Mark

Explanation of Solution

Given information:

  ABCD is a rhombus whose vertices are A(0,0),B(a,o),C(a+b,c),D(b,c) . Joining the diagonals AC and DB .

  McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 13.9, Problem 3WE

Calculation:

For a rhombus length of opposite sides are equal. That is,

  AB¯=aAD¯=b2+c2AB¯=AD¯a2=b2+c2.................(i)

Now if,

  Slope of AC¯=c0a+b0=ca+b=m1Slope of DB¯=c0ba=cba=m2

Then if both diagonal are perpendicular then it is sufficient to show : m1m2=1 , so that,

  m1m2=ca+b×cba=c2b2a2=c2c2=1   (From (i))

Hence it is proved that both diagonals are perpendicular to each other.

Chapter 13 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

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