SOLUTION: If CE bisects Angle DCB and CE is parallel to AB, Prove that angle A is congruent to Angle B Image: http://img154.imageshack.us/img154/7268/84057594cr6.png

Algebra ->  Geometry-proofs -> SOLUTION: If CE bisects Angle DCB and CE is parallel to AB, Prove that angle A is congruent to Angle B Image: http://img154.imageshack.us/img154/7268/84057594cr6.png      Log On


   

Question 176447: If CE bisects Angle DCB and CE is parallel to AB, Prove that angle A is congruent to Angle B

Image: http://img154.imageshack.us/img154/7268/84057594cr6.png
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Here's a better look at the image:




Here's a two column proof

StatementReason
1. Segment CE bisects Angle DCBGiven
2. Segment CE is parallel to Segment ABGiven
3. Angle DCE = Angle ECBDefinition of Angle Bisection (see statement 1)
4. Angle DCE = Angle CABCorresponding Angles/td>
5. Angle ECB = Angle ABCAlternate Interior Angles
6. Angle DCE = Angle ABCSubstitution (left side)
7. Angle CAB = Angle ABCSubstitution (left side)


Note: angle CAB is angle A and angle ABC is angle B