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. substitution property of equality
slope of segment de is −2 and slope of segment ac is −2.
segment de is parallel to segment ac. slopes of parallel lines are equal.
which is the missing justification?
additive identity
midsegment theorem
slope formula
transitive property of equality