Question

Use ΔABC to answer the question that follows.

Answer 1

Given: ΔABC

Prove: The three medians of ΔABC 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.

Answer 2

Statements Justifications
Point F is a midpoint of 1001_g5_q14a.gif Point # is a midpoint of 1001_g5_q14b.gif Draw 1001_g5_q14c.gif Draw 1001_g5_q14d.gif by Construction
Point G is the point of intersection between 1001_g5_q14e.gif and 1001_g5_q14f.gif Intersecting Lines Postulate
Draw 1001_g5_q14g.gif by Construction
Point D is the point of intersection between 1001_g5_q14h.gifand1001_g5_q13i.gif Intersecting Lines Postulate
Point H lies on 1001_g5_q14j1.gif such that 1001_g5_q14k.gif ≅ 1001_g5_q13l.gif by Construction
I 1001_g5_q14m.gif ≅ 1001_g5_q14n.gif Properties of a Parallelogram (diagonals bisect each other)
II 1001_g5_q14o.gifand 1001_g5_q14p.gif Midsegment Theorem
III 1001_g5_q14q.gifand 1001_g5_q14r.gif Substitution
IV BGCH is a parallelogram Properties of a Parallelogram (opposite sides are parallel)
1001_g5_q14s.gif is a median Definition of a Median