Given: Segment CE bisects <BCD; <A is congruent to <B
Prove: Segment CE ll to segment AB
-I used the exterior angle theorem to set the four angles equal to each other, but i don't know how to move on from there. The converse of something (maybe alternate interior angle) is important in proving it parallel also.
No idea where angle A or angle B is. Thought B was a point.
To prove that segment CE is parallel to segment AB, we can use the properties of angles formed by a transversal intersecting two parallel lines.
Given that segment CE bisects angle BCD and angle A is congruent to angle B, we can start by using the definition of angle bisector. The definition states that if a segment bisects an angle, then it divides the angle into two congruent angles.
So, in this case, we can say that angle BCE is congruent to angle DCE because segment CE bisects angle BCD. Similarly, angle A is congruent to angle B.
Now, let's consider the alternate interior angles formed by the transversal segment CE intersecting the lines AB and CD.
Angle BCE and angle A are alternate interior angles, and angle DCE and angle B are also alternate interior angles.
Since angle A is congruent to angle B (given), we can conclude that angle BCE is congruent to angle DCE using the transitive property of congruence.
Now, using the converse of the alternate interior angles theorem, which states that if two lines are cut by a transversal, and the alternate interior angles are congruent, then the lines are parallel, we can conclude that segment CE is parallel to segment AB.
Therefore, the statement that segment CE is parallel to segment AB is proved.