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

a) 0.25x times 3. (could be wrong on equation.)

b) 2.25 pound of dark chocolate. (can i eat all the chocolate? plz? anyway, again, could be wrong, but i hope im right. all the chocolate together should be 5.25 pounds)

have a good day!

the one that has a slope of 1/2 and is positive.

step-by-step explanation: 2 buckets 1 trip ; 4 buckets 2 trips and so on.