someone check my answers
http://prntscr.com/mls3hl

Question

Shadow · Answer

Your logic looks good to me.

8bithelix · Answer

although im unsure about 2 and 3

Shadow · Answer

For A, you can simply say that the lines are parallel because when Stacey turned 90 degrees to go from B->C, she didn't make any turns after going from C to D, thus we can conclude that DE is parallel to AB, as there are no notations of needing to turn for the trip from D to E, thus it is a straight line parallel to AB.

Shadow · Answer

For B, we already know angles B and D are congruent, which is stated in A so we can't repeat that in B. I do know that we can conclude that angle ACB and DCE are congruent. That is what makes it AA.

Shadow · Answer

Had to look up the name for it. It's vertical angles. You can review them here: https://mathbitsnotebook.com/Geometry/SegmentsAnglesTriangles/SATAnglePairs.html

Shadow · Answer

I believe that clears up 2 and 3

8bithelix · Answer

so i guess B is right?

Shadow · Answer

They both work, mine and yours, I just don't know the name for yours. With mine it's vertical pairs.

Shadow · Answer

But knowing the lengths is indicative of this being some sort of relationship.

Shadow · Answer

They are alternative interior angles. You can review those here: https://www.math10.com/en/geometry/angles/angles.html

Shadow · Answer

alternate interior*

Shadow · Answer

Because they are on alternate (opposite) sides of the transversal (AE) and in the interior (inside of both parallel lines, not outside, which would make them exterior).

Shadow · Answer

They are not adjacent to each other, and they are congruent, thus AA.

8bithelix · Answer

oh ok, thank you.