- Make valid congruence statements about two triangles.
- Discover and apply CPCTC (corresponding parts of congruent triangles are congruent).
- Use CPCTC to determine information about congruent triangles.
- Define the reflexive, transitive, and symmetric properties of congruence.
- Define and apply the three congruence transformations.
- Congruence Statement – A statement that tells which sides or angles of two triangles are congruent
- Congruence Transformation – An action that can be performed on a geometric object without changing its size or shape.
- After a congruence transformation, the perimeter of a triangle would be the same as it was before.
- Rotations (turns): rotating
- Translations (slides): translating
- Reflections (flips): reflecting
- Reflexive Property – The triangles are the exact same, with corresponding parts in the same order
- Symmetric Property – The triangles have been flipped (like in a mirror), so they are backwards from one another (like butterfly wings)
- Transitive Property – A syllogism (chain of events) involving triangles
- Congruent Triangles – Triangles with all congruent sides (equal in length) and all congruent corresponding angles (equal in measure).
- Congruent triangles have the same size and shape
- Congruent triangles have the same angle measures and side lengths
- The corresponding sides are congruent.
- The corresponding angles are congruent.
- CPCTC – Congruent Parts of Congruent Triangles are Congruent
- If 2 triangles are congruent, then all of their parts are congruent
- If all of the parts of two triangles are congruent, then the 2 triangles are congruent