As in the triangle aei: For they are both equall to one right angle, by the [13. e. vj]. And betweene themselves, by the [17. e. vj].
Therefore
6. If one angle of a triangle be equall to the other two, it is a right angle [And contrariwise Schon.]
Because it is equall to the halfe of two right angles, by the [13. e vj].
And
7. If a right line from the toppe of a triangle cutting the base into two equall parts be equall to the bisegment, or halfe of the base, the angle at the toppe is a right angle: [And contrariwise Schon.]
As in the triangle aei, the right line ao, cutting the base ei, in o, into two equall parts, is equall to eo, or oi, the halfe of the base maketh two equicrural triangles; and the severall angles at the top equall to the angles at the ends, viz. e, and i, by the [17. e. vj]. Therefore the angle at the toppe
is equall to the other two: wherefore by the [6 e], it is a right angle.