Theorem 9.1.4 (AAS Postulate)

Theorem 9.1.4: If in the correspondence of two right-angled triangles, the hypothenuse and one side of one triangle are congruent to the the hypothenuse and the corresponding side of the other, then the triangles are congruent.

Proof:

Given: $**\triangle ABC \leftrightarrow \triangle DEF$ $\angle B \cong \angle E$
$\overline{AC} \cong \overline{DF}$
$\overline{BC} \cong \overline{EF}$

To proof: $\triangle ABC \cong \triangle DEF$

Construction:** Produce $\overline{DE}$ to point $G$ such that $\overline{EG} \cong \overline{AB}$. Then join $F$ and $G$.

Proof: