4-1 Congruent Figures

Congruent Figures Whenever two figures have the same size and shape, they are called Congruent. We already know about congruent segments (segments that have equal lengths) and congruent angles (angles that have equal measure). Now we are going to learn about congruent triangles. Triangles ABC and DEF are congruent. If you mentally slide ABC to the right you can fit it exactly over DEF by matching up the vertices. A D B E C F A D F B E C

Congruent Figures The following statements are true: (1)Since congruent triangles have the same shape, their corresponding angles are congruent. (2) Since congruent triangles have the same size, their corresponding sides are congruent. Definition of congruent triangles: Two triangles are congruent if and only if their vertices can be matched up so that corresponding parts (sides and angles) of the triangle are congruent.

Congruent Triangles The congruent parts of the triangles shown are marked alike. What parts are congruent? When the definition of congruent triangles is used to justify either of these statements, the wording commonly used is Corresponding parts of congruent triangles are congruent (CPCTC) R U AS NY

Two polygons are congruent if and only if their vertices can be matched up so that their corresponding parts are congruent. Just as with triangles there are many ways to list the congruence between two pentagons. Notice that both polygons share side KE, that is called a common side. BRAKE = CHOKE R B E C H O A K