Mathematics, 09.11.2020 20:50 mayamabjishovrvq9

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) By the 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 By the distance formula
Segment DE is half the length of segment AC
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)

By definition of congruence
The converse of corresponding angles postulate
By substitution
By construction

Answers: 2

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