Mathematics, 09.09.2020 08:01 nemalipurim

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 a justification is missing.

A triangle with vertices A at 6, 8. B is at 2, 2. C is at 8, 4. Segment DE. Point D is on side AB and point E is on side BC

StatementJustification
The coordinates of point D are (4, 5) and coordinates of point E are (5, 3)Midpoint Formula
Length of segment DE is Square root of 5 and length of segment AC is 2 multiplied by the square root of 5 .Distance Formula
Segment DE is half the length of segment AC.
Slope of segment DE is −2 and slope of segment AC is −2.Slope Formula
Segment DE is parallel to segment AC. Slopes of parallel lines are equal.
Which is the missing justification? (6 points)

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