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Mathematics, 03.02.2020 07:43 tevaughn06

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

statement justification
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?
additive identity
by construction
midsegment theorem
substitution property of equality

ansver
Answers: 1

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