1. Objectives Use properties of congruent triangles.
Prove triangles congruent by using the definition of congruence.

2. Geometric figures are congruent if they are the same size and shape
Geometric figures are congruent if they are the same size and shape. ______________________ and _______________________are in the same position in polygons with an equal number of sides.
Two polygons are ________________if and only if their corresponding sides are congruent.
Thus triangles that are the same size and shape are congruent.

4. For example, P and Q are consecutive vertices.
Two vertices that are the endpoints of a side are called consecutive vertices.
For example, P and Q are consecutive vertices.
Helpful Hint

5. To name a polygon, write the vertices in consecutive order
To name a polygon, write the vertices in consecutive order. For example, you can name polygon PQRS as QRSP or SRQP, but not as PRQS.
In a congruence statement, the order of the vertices indicates the corresponding parts.

6. When you write a statement such as ABC  DEF, you are also stating which parts are congruent.
Helpful Hint

7. Example 1A: Naming Congruent Corresponding Parts
Given: ∆PQR  ∆STW
Identify all pairs of corresponding congruent parts.
Angles:
Sides:

8. Check It Out! Example 1B
If polygon LMNP  polygon EFGH, identify all pairs of corresponding congruent parts.
Angles:
Sides:

9. Example 2A: Using Corresponding Parts of Congruent Triangles
Given: ∆ABC  ∆DBC.
Find the value of x.

10. Example 2B: Using Corresponding Parts of Congruent Triangles
Given: ∆ABC  ∆DBC.
Find mDBC.

11. Check It Out! Example 2C
Given: ∆ABC  ∆DEF
Find the value of x.

12. Check It Out! Example 2D
Given: ∆ABC  ∆DEF
Find mF.