Question

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 through point H lying outside of triangle ABC. Line segments BH and CH are dashed 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 Point F is a midpoint of Line segment AB Point E is a midpoint of Line segment AC Draw Line segment BE Draw 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 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 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) IV, II, III, I II, IV, I, III IV, II, I, III II, IV, III, I

Answer 1

Answer:

c

Step-by-step explanation:

Median of triangle: It is a line segment joining a vertex to the midpoint of the opposite side.

Consider ΔABC, point F id the midpoint of line segment AB and E is the midpoint of luine segment AC.

Draw line segments FC and BE(medians of  triangle). G is the point where line segment FC and BE meet. Now, Join AG.

Let H be the point outside the ΔABC and AG passs through the point H  such that AG intersects BC at D. BH and HC are dashed lines.

We need to show that D is the midpoint of BC. The correct logical order for proof will be:

III. GC is parallel to line segment BH and line segment BG is parallel to line segment HC.

IV.  Line segment FG is parallel to line segment BH and line segment GE is parallel to line segment HC.

I. BGCH is a parallelogram as opposite sides are parallel (from III.)

II. Since, diagnols of a parallelogram bisect each other. Henc, we get BD=DC.

Therefore, D is mid pont of BC.

It implies that AD is also a median.

Hence, all the three medians that are: BE,FC and AD passes through a common vertex G.