91影视

Consider the figure.

If two lines are cut by a transversal line and the sum of two interior angles on the same side of the transversal is supplementary then those two lines are parallel.

Consider $鈭�ADC鈮�鈭�CBA;鈭�BAD鈮�鈭�DCB$.

Consider the angle sum property of quadrilateral as follows:

$\begin{array}{c}鈭�ADC+鈭�CBA+BAD+鈭�DCB={360}^{鈭�}\\ 2鈭�ADC+2鈭�DCB={360}^{鈭�}\\ 鈭�ADC+鈭�DCB={180}^{鈭�}\end{array}$

Since 鈥淚f two lines cut by a transversal line and sum of two interior angles on the same side of the transversal are supplementary then that two lines are parallel鈥� thus$\stackrel{炉}{AD}$is parallel to $\stackrel{炉}{BC}$ such that $\stackrel{炉}{AD}\left|\right|\stackrel{炉}{BC}$.

Similarly,

$\begin{array}{c}鈭�ADC+鈭�CBA+BAD+鈭�DCB={360}^{鈭�}\\ 2鈭�BAD+2鈭�ADC={360}^{鈭�}\\ 鈭�BAD+鈭�ADC={180}^{鈭�}\end{array}$

Since 鈥淚f two lines cut by a transversal line and sum of two interior angles on the same side of the transversal are supplementary then that two lines are parallel鈥� thus$\stackrel{炉}{AB}$is parallel to $\stackrel{炉}{DC}$ such that $\stackrel{炉}{AB}\left|\right|\stackrel{炉}{DC}$.

Thus, $ABCD$ is a parallelogram.