Prove that the segments joining the midpoints of the sides of any quadrilateral form a parallelogram.
Explanation of Solution
Given :
Calculation:
Locate the quadrilateral on the coordinate plane and assume the coordinates of the vertices.
Since A , B , C , and D are midpoints of RS, ST , TU , and UR respectively.
So, their coordinates are :
Slope of
Since , the slope of
Now, the lengths of
So,
So,
Hence , by Theorem 6.12 , ABCD is parallelogram.
Hence proved.
Chapter 6 Solutions
Geometry, Student Edition
Additional Math Textbook Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Elementary Statistics: Picturing the World (6th Edition)
College Algebra
Thomas' Calculus: Early Transcendentals (14th Edition)
Thinking Mathematically (7th Edition)
Precalculus (10th Edition)
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning