91Ó°ÊÓ

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped, and turned to be looked identical.

When two lines are cut by a transversal line and if the alternate interior angles are equal then lines are parallel.

Consider the figure.

Here the corresponding parts of $\mathrm{Δ}ABO$ and $\mathrm{Δ}CDO$ are congruent such that their corresponding angles and sides are equal such that $∠A=∠C$and $∠B=∠D$.

Since when a parallel line is cut by a transversal line then the alternate interior angle is equal thus $∠A=∠C$.

This implies that $\stackrel{¯}{DC}âˆ\yen \stackrel{¯}{AB}$and $AC$is a transversal line.

Therefore, this shows that $\stackrel{¯}{DC}âˆ\yen \stackrel{¯}{AB}.$