SOLUTION: please help me with this. THANK YOU so much. Given: angle AKE is congruent to angle REK. angle 1 is congruent to angle 4. Prove: segment SK is parallel to segment TE.

Algebra ->  Geometry-proofs -> SOLUTION: please help me with this. THANK YOU so much. Given: angle AKE is congruent to angle REK. angle 1 is congruent to angle 4. Prove: segment SK is parallel to segment TE.       Log On


   

Question 175998This question is from textbook Geometry
: please help me with this. THANK YOU so much.
Given: angle AKE is congruent to angle REK. angle 1 is congruent to angle 4.
Prove: segment SK is parallel to segment TE.
 This question is from textbook Geometry

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Does the figure look something like this:



If so, then here's a two column proof
StatementReason
1. Angle AKE = Angle REKGiven
2. Angle 1 = Angle 4Given
3. Angle 1 + Angle 2 = Angle AKEAngle Addition Postulate
4. Angle 3 + Angle 4 = Angle REKAngle Addition Postulate
5. Angle 1 + Angle 2 = Angle 3 + Angle 4Substitution (see statement 1)
6. Angle 4 + Angle 2 = Angle 3 + Angle 4Substitution
7. Angle 2 = Angle 3Addition Property of Equality
8. Segment SK is parallel to Segment TE Alternate Interior Angles Converse