## Elementary Geometry for College Students (6th Edition)

$\angle$BCE=$\frac{1}{2}$$\angleC \angleB+\angleC=180 \angleB+\angleBCE+\angleBEC=180 \angleB+\frac{1}{2}$$\angle$C+$\angle$BEC=180 $\angle$B+$\frac{1}{2}$$\angleC+\angleBEC=\angleB+\angleC \angleBEC=\frac{1}{2}$$\angle$C Since two angles have a measure equal to half of angle C, it must be an equilateral triangle.