SSS and SAS Theorems

Learning Objectives Define the Side-Side-Side (SSS) and Side-Angle-Side (SAS) congruence postulates. Identify corresponding sides and angles in a pair of triangles from a diagram. Determine if the SSS Postulate can be used to prove two triangles are congruent. Determine if the SAS Postulate can be used to prove two triangles are congruent, paying special attention to the included angle. Write a formal geometric proof using the SSS and SAS postulates. Distinguish between the valid SAS postulate and the invalid SSA condition. Apply the Reflexive Property of Congruence to identify shared sides or angles in a proof. Ever wonder how engineers build massive, stable bridges or towering cranes that don't collapse? 🌉 The secret lies in the rigid strength of triangles! In thi...

TermDefinitionExample Congruent TrianglesTwo triangles are congruent if all three of their corresponding sides and all three of their corresponding angles are equal. In essence, they are exact copies of each other.If \triangle ABC \cong \triangle XYZ, it means \overline{AB} \cong \overline{XY}, \overline{BC} \cong \overline{YZ}, \overline{AC} \cong \overline{XZ}, and \angle A \cong \angle X, \angle B \cong \angle Y, \angle C \cong \angle Z. Corresponding PartsThe matching sides and angles in two congruent triangles. The order of the vertices in a congruence statement tells you which parts correspond.In the statement \triangle CAT \cong \triangle DOG, \angle A corresponds to \angle O, and side \overline{CT} corresponds to side \overline{DG}. Side-Side-Side Postulate (SSS)A rule stating tha...

Side-Side-Side (SSS) Congruence Postulate If \overline{AB} \cong \overline{DE}, \overline{BC} \cong \overline{EF}, and \overline{AC} \cong \overline{DF}, then \triangle ABC \cong \triangle DEF. Use this rule when you can show that all three pairs of corresponding sides of two triangles are equal in length. You don't need any information about the angles. Side-Angle-Side (SAS) Congruence Postulate If \overline{AB} \cong \overline{DE}, \angle B \cong \angle E, and \overline{BC} \cong \overline{EF}, then \triangle ABC \cong \triangle DEF. Use this rule when you can show that two pairs of corresponding sides are equal, AND the angle *between* those two sides is also equal. The position of the angle is critical.