# geometry

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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

• geometry -

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)

• geometry -

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

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