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.

Question

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

Answer 1

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)

Answer 2

line RS=line UT and line RT= line US
prove triangle RST= triangle UTS