Congruent triangles: SSS, SAS, and ASA

Learning Objectives Define triangle congruence and identify corresponding parts. Explain the Side-Side-Side (SSS) Postulate and use it to prove triangles are congruent. Explain the Side-Angle-Side (SAS) Postulate and use it to prove triangles are congruent. Explain the Angle-Side-Angle (ASA) Postulate and use it to prove triangles are congruent. Analyze given information to determine which congruence postulate (SSS, SAS, or ASA) applies to a pair of triangles. Write a formal congruence statement, ensuring vertices are in the correct corresponding order. Use congruence to determine unknown side lengths or angle measures in a triangle. Have you ever wondered how manufacturers produce thousands of identical phone screens or how engineers build massive, stable bridges? 🌉 It a...

TermDefinitionExample Congruent TrianglesTwo triangles are congruent if all three of their corresponding sides are equal in length and all three of their corresponding angles are equal in measure. Essentially, they are identical in size and shape.If \triangle ABC has sides of 3, 4, 5 and angles of 90°, 53.1°, 36.9°, and \triangle XYZ has the same measurements, then \triangle ABC is congruent to \triangle XYZ. Corresponding PartsThe matching sides and angles in two congruent triangles. If \triangle ABC \cong \triangle DEF, then \angle A corresponds to \angle D, side AB corresponds to side DE, and so on.In the statement \triangle CAT \cong \triangle DOG, the corresponding angle to \angle C is \angle D, and the corresponding side to segment AT is segment OG. Side (S)A line segment that forms...

Side-Side-Side (SSS) Postulate If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. Use this when you know the lengths of all three sides for both triangles. If side 1, side 2, and side 3 of the first triangle match side 1, side 2, and side 3 of the second, you can declare them congruent. For \triangle ABC and \triangle DEF, if AB \cong DE, BC \cong EF, and CA \cong FD, then \triangle ABC \cong \triangle DEF. Side-Angle-Side (SAS) Postulate If two sides and the *included* angle of one triangle are congruent to two sides and the *included* angle of another triangle, then the two triangles are congruent. Use this when you have information about two sides and the angle *between them*. The position of the angle is...