1. Congruent Triangles Congruent Triangles – Triangles that are the same size and same shape.  ABC is congruent to  DEF, therefore:  A cong. to  Dseg. AB cong. to seg. DE  B cong. to  Eseg. BC cong. to seg. EF  C cong. to  Fseg. AC cong. to seg. DF

2. Congruent Triangles If all six of the corresponding parts of two triangles are congruent, then the triangles are congruent. Likewise, if two triangles are congruent, then all six of the corresponding parts of the triangles are congruent. Corresponding Parts of Congruent Triangles are Congruent (CPCTC) – Two triangles are congruent if and only if their corresponding parts are congruent.

3. Example 3-1c Answer: The support beams on the fence form congruent triangles. b. Name the congruent triangles. a. Name the corresponding congruent angles and sides of  ABC and  DEF. Answer:  ABC  DEF

4. Congruent Triangles Theorem 4.4 Congruence of triangles is reflexive, symmetric, and transitive. Reflexive:  ABC is congruent to  ABC Symmetric: If  ABC is congruent to  DEF, then  DEF is congruent to  ABC. Transitive: If  ABC is congruent to  DEF and  DEF is congruent to  GHI, then  ABC is congruent to  GHI.

5. Congruent Triangles Transformation – A redrawing of a figure in the same plane such that each point of the image corresponds to exactly one point of the original. Congruence Transformations – Certain types of transformations that preserve the size and shape of the triangle. Slide (Translation), Flip (Reflection), Turn (Rotation)

6. Example 3-2f COORDINATE GEOMETRY The vertices of  ABC are A(–5, 5), B(0, 3), and C(–4, 1). The vertices of  ABC are A(5, –5), B(0, –3), and C(4, –1). Answer: Use a protractor to verify that corresponding angles are congruent. a. Verify that  ABC  ABC.

7. Example 3-2g Answer: turn b. Name the congruence transformation for  ABC and  ABC.