Given: ∆ABC

Prove: The three medians of ∆ABC intersect at a common point.

When written in the correct order, the two-column proof below describes the statements and justifications for proving the three medians of a triangle all intersect in one point

Question

Given: ∆ABC

Prove: The three medians of ∆ABC intersect at a common point.

When written in the correct order, the two-column proof below describes the statements and justifications for proving the three medians of a triangle all intersect in one point

anonymous · Answer

Statements Justifications 
 Point F is a midpoint of  
Point E is a midpoint of  
Draw  
Draw   by Construction 
 Point G is the point of intersection between  and   Intersecting Lines Postulate 
 Draw   by Construction 
 Point D is the point of intersection between  and   Intersecting Lines Postulate 
 Point H lies on  such that  ≅   by Construction 
 I BGCH is a parallelogram Properties of a Parallelogram (opposite sides are parallel) 
 II  ≅   Properties of a Parallelogram (diagonals bisect each other) 
 III  and   Substitution 
 IV  and   Midsegment Theorem 
  is a median Definition of a Median