91Ó°ÊÓ

Consider the figure.

The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

The Side-Side-Side Postulate (SSS) says triangles are congruent if three sides of one triangle are congruent to the corresponding sides of the other triangle.

SAS Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.

Consider that $\stackrel{¯}{AB}\left|\right|\stackrel{¯}{DC};\stackrel{¯}{AB}â‰\dots \stackrel{¯}{DC}$.

Reason 1. It is given that $\stackrel{¯}{AB}â‰\dots \stackrel{¯}{DC}$.

Reason 2. Reflexive property such that $\stackrel{¯}{AC}â‰\dots \stackrel{¯}{DC}$.

Reason 3. It is given that $\stackrel{¯}{AB}\left|\right|\stackrel{¯}{DC}$.

Reason 4. Alternate interior angles are congruent such that $∠BACâ‰\dots ∠DCA$.

Reason 5. SAS postulate $\mathrm{Δ}ABCâ‰\dots \mathrm{Δ}CDA$

Thus, the triangles are congruent with the SAS postulate.