Posted: May 17th, 2022

Intersect at a Common Point Assignment | Assignment Help Services

Use ΔABC to answer the question that follows:

Triangle ABC. Point F lies on AB. Point D lies on BC. Point E lies on AC. AD, BE, and CF passes through point G. Line AD passes

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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:

Statements Justifications

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Point F is a midpoint of Line segment AB Point E is a midpoint of Line segment AC Draw Line segment BEDraw Line segment FC by Construction

Point G is the point of intersection between Line segment BE and Line segment FC Intersecting Lines Postulate

Draw Line segment AG by Construction

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Point D is the point of intersection between Line segment AG and Line segment BC Intersecting Lines Postulate

Point H lies on Line segment AG such that Line segment AG ≅ Line segment GH by Construction

I BGCH is a parallelogram Properties of a Parallelogram (opposite sides are parallel)

II Line segment FG is parallel to line segment BH and Line segment GE is parallel to line segment HC Midsegment Theorem

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III Line segment BD ≅ Line segment DC Properties of a Parallelogram (diagonals bisect each other)

IV Line segment GC is parallel to line segment BH and Line segment BG is parallel to line segment HC Substitution

Line segment AD is a median Definition of a Median

Which is the most logical order of statements and justifications I, II, III, and IV to complete the proof? (4 points)

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II, IV, III, I

II, IV, I, III

IV, II, III, I

IV, II, I, III Get Math homework help

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