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

Segment DE is half the length of segment AC.-- Substitution property of equality

Step-by-step explanation:

Here is given a proof for proving line joining mid segment is parallel and half the length of third side.

Stepwise proof is given in two columns

We find that for every line there is a justification as

STatement                                        Justification

D and E coordinates found out       MId point formula

DE and BC are measured                Distance formula

DE=1/2 BC                                          Substitution property of equality

This justification was missing in the given proof and with this included proof would be complete

substitution property of equality

Step-by-step explanation:

i took the exam and got it right

Line M - neither

Line N - perpendicular

Line P - neither

Line Q - parallel

Step-by-step explanation:

A line that is perpendicular will aways have and opposite slope, e.g. -3/4, opposite, 4/3.

A line that is parallel will always have the exact same slope, e.g. -3/4, same, -3/4.