Theorem 9.1.3 (SSS Postulate)

Theorem 9.1.3: In a correspondence of two triangles, if three sides of one triangle are congruent to the corresponding three sides of the other, the two triangles are congruent.

Given: In $\triangle ABC \leftrightarrow \triangle DEF$ $\overline{AB} \cong \overline{DE}$, $\overline{BC} \cong \overline{EF}$ & $\overline{CA} \cong \overline{FD}$

To prove:
$\triangle{ABC} \cong \triangle{DEF}$

Construction: Suppose that $\overline{BC}$ is the largest side of triangle $\triangle ABC$. Construct triangle $\triangle GEF$ such that: i. Point $G$ ii. $\angle FEG \cong \angle B$ iii. $\overline{EG} \cong \overline{BA}$

Then join D and G.

Proof:

Corollary: The angles of an equilateral triangle are equal in measurement.

Given: $\Delta ABC$ be an equilateral triangle. $∴\overline{AB} = \overline{BC} = \overline{CA}$

To Prove: $\angle A = \angle B = \angle C$

Construction: Draw bisector line from $\angle A$ to side $\overline{BC}$, a bisector line from $\angle B$ to side $\overline{CA}$

Proof:

Common Mistakes:

• AAA (Angle-Angle-Angle) Postulate does not exist.