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.

The corresponding parts of congruent triangle are congruent.

Consider $AT=CT;DT=\frac{1}{2}DB$.

Consider the triangles $螖ATB,螖CTD$ and thus

Since $鈭�ATB$ and $鈭�CTD$ are vertically opposite angles thus they are equal such that $鈭�ATB=鈭�CTD$.

Use the SAS postulate as follows:

$螖ATB鈮�螖CTD$

Since corresponding part of congruent triangle are congruent such that .

$螖ATB鈮�螖CTD$

Thus $AS=BQ$.

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$\stackrel{炉}{AB}\left|\right|\stackrel{炉}{DC}$ .

Since corresponding part of congruent triangle are congruent such that .

$螖BAT鈮�螖DCT$

Thus, ABCD is a parallelogram.