Mathematics, 04.11.2019 22:31 perryjarvisr1751

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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

(image attached for info down below in case it's too confusing to read)

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 .

segment de is half the length of segment ac.

substitution property of equality 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)

a. additive identity

b. distance formula

c. midsegment theorem

d. transitive property of equality

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