Theorem 9.1.1 (ASA Postulate)

Theorem 9.1.1 (A.S.A Postulate): In any correspondence of two triangles, if one side and two angles of one triangle are congruent to the corresponding sides and angles of the other, the two triangles are congruent.

Proof:

Given :

In $\Delta ABC\leftrightarrow \Delta PQR$, then

$\angle B\cong \angle Q, m\overline{BC}\cong m\overline{QR},$ and $\angle A\cong \angle P$

To Prove:

$\Delta ABC \cong \Delta PQR$

Construction:

Suppose, $\overline{AB} \not\cong \overline{PQ}$ take a point $P^{\prime}$ on PQ such that $AB = P^{\prime}Q$

Proof: