1. Warm-Up What does it mean for two triangles to be congruent?
If a contractor was building a house, how could she or he check to see if all of the roof trusses, which are triangles, were identical?

2. Warm-Up What does it mean for two triangles to be congruent?
If a contractor was building a house, how could she or he check to see if all of the roof trusses, which are triangles, were identical?

3. 4.2 and 4.3 Congruent Triangles and SSS
Apply Congruence and Triangles Prove Triangles Congruent by SSS and SAS
Objectives:
To define congruent triangles
To write a congruent statement
To prove triangles congruent by SSS and SAS

4. Congruent Polygons

5. Congruent Triangles (CPCTC)
Two triangles are congruent triangles if and only if the corresponding parts of those congruent triangles are congruent.
Corresponding sides are congruent
Corresponding angles are congruent

6. Congruence Statement
When naming two congruent triangles, order is very important.

7. Example 1
Write a congruence statement for the congruent triangles below.

8. Example 2
Which polygon is congruent to ABCDE?
ABCDE  -?-

9. Example 3
Locate points I and S so that BLUE  FISH. S I

10. Properties of Congruent Triangles

11. Example 4
What is the relationship between <C and <F?

12. Third Angle Theorem
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

13. Example 5
Now back to the subject of roof trusses. Would it be necessary for the manufacturer of a set of trusses to check that all the corresponding angles were congruent as well as the sides?

14. Example 5
In other words, is it sufficient that the pieces of wood (the sides of each triangle) are all the same length?

15. Congruence Shortcuts Side-Side-Side (SSS) Congruence Postulate:
If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

16. Congruence Shortcuts Side-Angle-Side (SAS) Congruence Postulate:
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

17. Side-Side-Side Congruence Postulate
SSS Congruence Postulate:
If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

18. SSS Congruence Postulate

19. Example 6
Decide whether the triangles are congruent. Explain your reasoning.

20. Example 7

26. Example 8
Explain why the bench with the diagonal support is stable, while the one without the support can collapse.