Lesson 4-1 Congruent Figures

1. B E C F D A Chapter 4 Corresponding Parts in a Congruence Lesson 4-1Congruent Figures When two figures have the same size and shape, they are congruent. 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.

2. B E C F D A The corresponding parts match up like this: Corresponding angles A and D B and E C and F Corresponding sides AB and DE BC and EF AC and DF

3. B E C F D A We can see that the following statements are true: • 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. This gives us the definition for congruent triangles.

4. B E C F D A When we are referring to congruent triangles, we name their corresponding vertices in order. Using the example from above with triangles ABC and DEF, ABC DEF, CABFDE, and BCAEFD are all true statements.

5. B E C F D A Two triangles are congruent if and only if their vertices can be matched up so that the corresponding parts (angles and sides) of the triangles are congruent.

6. When the definition of congruent triangles is used to justify either the congruence of individual angles or sides, the wording commonly used is: Corresponding parts of congruent triangles are congruent or Corresponding Parts of s are  Two polygons are congruent if and only if their vertices can be matched up so that their corresponding parts are congruent.

7. M N L P MP is the common side of the triangles LMP and NMP. If two polygons share a side, it is called the common side.