91Ó°ÊÓ

The given diagram is:

Definition of parallelogram states that a parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.

It can be seen that $\stackrel{¯}{AD}âˆ\yen \stackrel{¯}{BC}$.

From the given diagram it can be noticed that $\stackrel{¯}{AD}$ and$\stackrel{¯}{BC}$ are the opposite sides of the quadrilateral ABCD.

As, $\stackrel{¯}{AD}âˆ\yen \stackrel{¯}{BC}$, therefore it can be said that the opposite sides of the quadrilateral ABCD are parallel.

Therefore, it can be said that $\stackrel{¯}{AD}âˆ\yen \stackrel{¯}{BC}$by using the definition of a parallelogram.

Theorem 3-2 states that if two parallel lines are cut by a transversal, then alternate interior angles are congruent.

Now, as the lines $\stackrel{¯}{AD}$ and $\stackrel{¯}{BC}$ are parallel lines and there is a transversal BD, therefore the angles$∠ADX$and $∠CBX$are the alternate interior angles.

Therefore, by using the theorem 3-2, it can be said that the angles $∠ADX$and $∠CBX$are congruent.

Therefore,$∠ADXâ‰\dots ∠CBX$

Therefore, the definition and theorem that justifies the statement $∠ADXâ‰\dots ∠CBX$is the definition of the parallelogram which states that a parallelogram is a quadrilateral in which both pairs of opposite sides are parallel, and the theorem 3-2 states that if two parallel lines are cut by a transversal, then alternate interior angles are congruent.