1. Chapter 5
Congruent Triangles

2. Section 1 Congruence and Triangles

3. The houses below are located in San Francisco, California
The houses below are located in San Francisco, California. The two triangles outlined on the houses have the same size and shape. Suppose ∆𝐴𝐵𝐶 slides over to fit on ∆𝐷𝐸𝐹. When the vertices are matched this way, <A and <D are corresponding angles and AC and DF are corresponding sides.

4. Corresponding angles and corresponding sides are examples of ___________________________________________________. Figures are ______________________________ if all pairs of corresponding angles are congruent and all pairs of corresponding sides are congruent.

5. Example 1: List Corresponding Parts Angles Sides

6. Example 2: Write a Congruence Statement
The two triangles are congruent.
Identify all corresponding congruent parts.
Angles Sides
b) Write a congruence statement.

7. Example 3: Use Properties of Congruent Triangles
In the diagram, ∆𝑃𝑄𝑅≅∆𝑋𝑌𝑍.
Find the length of XZ.
Find m<Q.

8. Checkpoint: Name Corresponding Parts and Congruent Triangles 1) 2) 3)

9. Example 4: Determine Whether Triangles are Congruent
Use the two triangles at the right.
Identify all corresponding congruent parts.
Determine whether the triangles are congruent. If they are congruent, write a congruence statement.

10. Example 5: Determine Whether Triangles are Congruent In the figure, HG || LK. Determine whether the triangles are congruent. If so, write a congruence statement.

11. Checkpoint: Determine Whether Triangles are Congruent In the figure, XY || ZW. Determine whether the two triangles are congruent. If they are, write a congruence statement.

12. EXIT SLIP