Provide the missing reasons for the proof of part of the triangle midsegment theorem. given: k is the midpoint of line mj. l isthe midpoint of line nj. prove mn =2kl

statement:
1. k is the midpoint of line mj. l is the midpoint of line nj
2. line mk is parallel to line kj and line nl is parallel to line lj
3. mk = kj and nl = lj
4. mj =mk +kj and nj = nl+lj
5. mj = 2kl and nj = 2lj
6. mj/kj = nj/lj = 2
7. angle j is parallel to angle j
8.triangle jmn is congruent to triangle jkl
9. mn/kl = mj/kj
10. mn/kl = 2
11. mn = 2kl

reason:
1.
2
3.
4.
5. substitution property of equality
6. division property of equality
7.
8.
9.
10.
11.

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.

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step-by-step explanatio89

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1