Proving triangles congruent by ASA and AAS

Learning Objectives Identify the included side between two angles in a triangle. Differentiate between the Angle-Side-Angle (ASA) Postulate and the Angle-Angle-Side (AAS) Theorem. Determine if ASA or AAS can be used to prove two triangles are congruent based on given information. Write a formal two-column proof to show triangle congruence using the ASA Postulate. Construct a logical argument in a two-column proof to demonstrate triangle congruence using the AAS Theorem. Apply ASA and AAS congruence to solve for unknown side lengths or angle measures in geometric figures. How can engineers guarantee that a triangular bridge support is stable and identical to others without measuring every single part? 🌉 It's all about geometric shortcuts! This tutorial will teach you t...

TermDefinitionExample Congruent TrianglesTwo triangles are congruent if all three corresponding sides and all three corresponding angles are equal in measure. Essentially, they are exact copies of each other.If \triangle ABC \cong \triangle DEF, then \angle A \cong \angle D, \angle B \cong \angle E, \angle C \cong \angle F, \overline{AB} \cong \overline{DE}, \overline{BC} \cong \overline{EF}, and \overline{AC} \cong \overline{DF}. Included SideThe side of a triangle that is located between two specified angles.In \triangle XYZ, the side \overline{XY} is the included side between \angle X and \angle Y. Non-included SideA side of a triangle that is not located between two specified angles.In \triangle XYZ, the side \overline{YZ} is a non-included side for the pair of angles \angle X and \an...

Angle-Side-Angle (ASA) Congruence Postulate Given \triangle ABC and \triangle DEF. If \angle A \cong \angle D, \overline{AC} \cong \overline{DF}, and \angle C \cong \angle F, then \triangle ABC \cong \triangle DEF. Use this when you can prove that two pairs of corresponding angles and the side *between* them are congruent. The 'S' is physically located between the two 'A's in the triangle. Angle-Angle-Side (AAS) Congruence Theorem Given \triangle ABC and \triangle DEF. If \angle A \cong \angle D, \angle B \cong \angle E, and \overline{BC} \cong \overline{EF}, then \triangle ABC \cong \triangle DEF. Use this when you can prove that two pairs of corresponding angles and a side that is *not* between them are congruent. The 'S' is adjacent to only o...