Rules of Triangles Congruence
The Side-Angle-Side postulate guarantees that two given triangles are congruent if:
* Two of their sides are congruent
* The angle included between them is congruent with the corresponding angle
We are given the figure EBEX and it's known that the segment XB bisects angle EBW. Assuming EB and BW are congruent (they have the same length), then:
1. Segment XB is common to both triangles
2. Segments EB and BW are conguent
3. Angles EBX and WBX are congruent because they are halved by the bisector.
4. Since we have two congruent sides and their included angle is congruent, then both triangles are congruent.
5. Angles E and W are corresponding thus they are congruent.
It follows that measure of