Moreover, if \((AB) \ne (CD)\), then in the first case, \(A\) and \(D\) lie on opposite sides of \((BC)\); in the second case, \(A\) and \(D\) lie on the same sides of \((BC)\). Therefore \(2 \cdot \m...Moreover, if \((AB) \ne (CD)\), then in the first case, \(A\) and \(D\) lie on opposite sides of \((BC)\); in the second case, \(A\) and \(D\) lie on the same sides of \((BC)\). Therefore \(2 \cdot \measuredangle BCD \equiv 2 \cdot BCD'\) and by Exercise 2.4.2, \(D' \in (CD)\), or equivalently the line \((CD)\) coincides with \((CD')\). Finally, if \((AB) \ne (CD)\) and \(A\) and \(D\) lie on the opposite sides of \((BC)\), then \(\angle ABC\) and \(\angle BCD\) have opposite signs.
