91影视

The given figure is:

It is being given that $AX鈮�CY$, $鈭�A鈮�鈭�C$, $\stackrel{炉}{BX}鈯�\stackrel{炉}{AD}$and $\stackrel{炉}{DY}鈯�\stackrel{炉}{BC}$.

As, $\stackrel{炉}{BX}鈯�\stackrel{炉}{AD}$, therefore$鈭�AXB=90掳$.

As, $\stackrel{炉}{DY}鈯�\stackrel{炉}{BC}$, therefore $鈭�CYD=90掳$.

Therefore, it is obtained that $鈭�AXB=鈭�CYD$.

Therefore, $鈭�AXB鈮�鈭�CYD$

Therefore, in the triangles $螖ABX$and $螖CDY$, it can be noticed that$鈭�AXB鈮�鈭�CYD$,$AX鈮�CY$and $鈭�A鈮�鈭�C$.

Therefore, $螖ABX鈮�螖CDY$by using ASA postulate.

Therefore, by using the corresponding parts of congruent triangles it can be noticed that $\stackrel{炉}{BX}鈮�\stackrel{炉}{DY}$.

In the triangles $螖BDX$and $螖DBY$, $DB$is the hypotenuse, $\stackrel{炉}{BX}$and $\stackrel{炉}{DY}$are the legs.

Therefore, by using the HL theorem it can be said that $螖BDX鈮�螖DBY$.

Therefore, by using the corresponding parts of congruent triangles it can be noticed that $鈭�1鈮�鈭�2$.

If the lines are cut by a transversal then if the alternate interior angles are congruent then lines are parallel.

Therefore, as the alternate interior angles $鈭�1$and $鈭�2$ are congruent, therefore the lines $\stackrel{炉}{AD}$and$\stackrel{炉}{BC}$are parallel.

The reason for each key step of the proof is: