Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. A two-c
olumn proof of the theorem is shown, but the proof is incomplete. A triangle with vertices A is at 6, 8. B is at 2, 2. C is at 8, 4. Segment DE with point D on side AB and point E is on side BC Statement Reason The coordinates of point D are (4, 5) and coordinates of point E are (5, 3) Length of segment DE is Square root of 5 and length of segment AC is 2 multiplied by the square root of 5 By the distance formula Segment DE is half the length of segment AC By substitution Slope of segment DE is −2 and slope of segment AC is −2 By the slope formula Segment DE is parallel to segment AC Slopes of parallel lines are equal Which of the following completes the proof? (6 points) Select one: a. By the midpoint formula b. By definition of congruence c. Given d. By construction
#1 The ALTITUDE is
a line segment that connects a vertex of a triangle to a point on the
line containing the opposite side, so that the line segment is perpendicular to that line.
#2 The MEDIAN a line segment that connects a vertex of a triangle to the midpoint of the opposite side
