geometry
posted by josh .
I have triangle XYZ with BX as the bisector sides XY and XZ are congruent. I have to write a proof for angle Y being congruent to angle Z.
This is what I have, but it doesn't seem correct  can anyone help?
XY is congruent to XZ  Given
XB bisects angle XYZ  Perpendicular Bisector of Isosceles Triangle
YB is congruent to BZ  Don't know why
XB is congruent to XB  Reflexive Prop
XBY is congruent to XBZ  SSS Theorem
Angle Y is congruent to Angle Z  CPCTC

You want to use ASA, not SSS
I would write it this way
XY is congruent to XZ  Given
angle YXB = angle ZXB  given angle x is bisected
XB = XB reflexise prop.
then triangle XYB is congruent to triangle XZB (ASA)
therefore angle Y = angle Z (properties of congruent triangles) 
line RS=line UT and line RT= line US
prove triangle RST= triangle UTS