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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 βˆ’2 and slope of segment AC is βˆ’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)

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Answers: 1

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Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side...
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