Question 176065: This proof is very hard to explain and is a weird figure!!! Please try to follow me on this. This proof is also very long. I would appreciate it so much if you take your time to read this. Im sorry to bother you, please try your best, and email if you do or do not know the answer. Thank you.
Given: Angle AKE is congruent to Angle REK
Angle 1 is congruent to Angle 4
Prove: Line SK is parallel to Line TE.
First of all, there is two lines, Line S is a straight line above Line T. They look parallel already. Next, point K is on Line S, bout in the middle of it. And point E is about almost to the end of the line on the right hand side of Line T. This is were it gets confusing. Point A is above and to the right of point K, about a 45 degree angle, if you draw an imaginary line right above point K. From point K there is a segment that goes down to connect to point E. And from point E, the line goes down to point R which is below line T, but directly in line with point K. Angle 1 is the first angle made at the top, and Angle 2 is right below it, and then Angles 3 and 4 are where K and E meet and where E drops down to meet R. 3 is above 4.
I know this a long proof, and please help me, i really need help, because if i dont get this proof right, i will fail my exam, because it is a take home proof. THANK YOU 4 YOUR TIME.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I've answered this before, so please let me know if you've already got this solution. If you have questions, feel free to ask me.
Does the figure look something like this:
If so, then here's a two column proof
| Statement | Reason |
| 1. Angle AKE = Angle REK | Given |
| 2. Angle 1 = Angle 4 | Given |
| 3. Angle 1 + Angle 2 = Angle AKE | Angle Addition Postulate |
| 4. Angle 3 + Angle 4 = Angle REK | Angle Addition Postulate |
| 5. Angle 1 + Angle 2 = Angle 3 + Angle 4 | Substitution (see statement 1) |
| 6. Angle 4 + Angle 2 = Angle 3 + Angle 4 | Substitution |
| 7. Angle 2 = Angle 3 | Addition Property of Equality |
| 8. Segment SK is parallel to Segment TE | Alternate Interior Angles Converse |
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