Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Congruent Triangles Congruent Triangles – Triangles that are the same size and same shape. ABC is congruent to DEF, therefore: A cong. to D B cong. to E C cong. to F seg. AB cong. to seg. DE seg. BC cong. to seg. EF seg. AC cong. to seg. DF 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. The support beams on the fence form congruent triangles. a. Name the corresponding congruent angles and sides of ABC and DEF. Answer: b. Name the congruent triangles. Answer: ABC DEF 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. 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) 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). a. Verify that ABC ABC. Answer: Use a protractor to verify that corresponding angles are congruent. b. Name the congruence transformation for ABC and ABC. Answer: turn