Proving triangles congruent by SSS and SAS

Learning Objectives Define triangle congruence and identify corresponding parts. State and apply the Side-Side-Side (SSS) Congruence Postulate. State and apply the Side-Angle-Side (SAS) Congruence Postulate. Distinguish between an included angle and a non-included angle in a triangle. Write formal two-column proofs to prove triangles are congruent using SSS and SAS. Use given information from diagrams and text to determine which congruence postulate to apply. Identify implicit information in a diagram, such as shared sides (Reflexive Property) or vertical angles. How does a manufacturer produce thousands of identical smartphone parts or a builder create perfectly matched roof trusses? 🏗️ They rely on the geometric principle of congruence! This tutorial will teach you two...

TermDefinitionExample Congruent TrianglesTwo triangles are congruent if and only if their corresponding sides and corresponding angles are congruent. This means they have the exact same size and shape.If \(\Delta ABC \cong \Delta DEF\), it means \(\overline{AB} \cong \overline{DE}\), \(\overline{BC} \cong \overline{EF}\), \(\overline{AC} \cong \overline{DF}\), and \(\angle A \cong \angle D\), \(\angle B \cong \angle E\), \(\angle C \cong \angle F\). 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 \(\Delta PQR \cong \Delta XYZ\), \(\angle P\) corresponds to \(\angle X\), and side \(\overline{QR}\) corresponds to side \(\overline{YZ}\). Side-Side-Side (SSS) Post...

Side-Side-Side (SSS) Congruence Postulate Given \(\Delta ABC\) and \(\Delta DEF\), if \(\overline{AB} \cong \overline{DE}\), \(\overline{BC} \cong \overline{EF}\), and \(\overline{AC} \cong \overline{DF}\), then \(\Delta ABC \cong \Delta DEF\). Use this postulate when you can show that all three pairs of corresponding sides of two triangles are congruent. This is often used when you are given lengths or see tick marks indicating all three sides are congruent. Side-Angle-Side (SAS) Congruence Postulate Given \(\Delta ABC\) and \(\Delta DEF\), if \(\overline{AB} \cong \overline{DE}\), \(\angle B \cong \angle E\), and \(\overline{BC} \cong \overline{EF}\), then \(\Delta ABC \cong \Delta DEF\). Use this postulate when you can show two pairs of corresponding sides are congruent,...