Problem: Given triangle with medians parallel and equal to and are drawn; extended meets in . Which one of the following statements is not necessarily correct?
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Answer Choices:
A. is a parallelogram
B.
C.
D.
E. is a median of triangle
Solution:
(A) is true because is parallel and equal to . (C) is true because when , which is parallel to , is extended, it meets in and are corresponding sides of congruent triangles and HDB. (D) is true because
( E ) is true because is the midpoint of . ( is parallel to and is the midpoint of .) (B) cannot be proved from the given information. Challenge: What additional information is needed to prove (B)?