Mathematics, 04.12.2020 23:50 henbry540
Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
A two-column 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)
Answers: 1
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