1) [tex]\overline{UT}[/tex]
2) [tex]\overline{UT} \cong \overline{UT}[/tex]
3) [tex]\overline{BT} \cong \overline{EU}[/tex]
4) [tex]\overline{BU} \cong \overline{ET}[/tex]
5) [tex]\triangle UBT \cong \triangle TEU[/tex] by SSS
6) CPCTC
