1. 6. Congruence Table of Contents

2. Congruence Essential Question – What is congruence and how do you show triangles are congruent?

3. Symbol for congruent

4. Naming a side

5. Naming an angle

6. Congruence marks Identify congruent segments in a diagram For line segments, they are shown with tic marks For angles, they are shown with an arc B A C D

7. Parts of a Right Triangle Leg Hypotenuse

8. Parts of an Isosceles Triangle Leg Base __ ___

9. Vertical angles Vertical angles are equal

10. Shared side If triangles share a side, the shared side is equal

11. Congruent Figures 2 figures are congruent if they have the exact same size and shape (all angles are equal and all sides are equal2 figures are congruent if they have the exact same size and shape (all angles are equal and all sides are equal Triangle ABC is congruent to Triangle DEFTriangle ABC is congruent to Triangle DEF

12. YZ Corresponding parts When 2 figures are congruent the corresponding parts are congruent. (angles and sides)When 2 figures are congruent the corresponding parts are congruent. (angles and sides) If Δ ABC is  to Δ XYZ, which side is  to BC?If Δ ABC is  to Δ XYZ, which side is  to BC?

13. Proving triangles are congruent There are several ways to prove that triangles are congruent, we will learn them over the next 2 days

14. Side-Side-Side (SSS) If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent.

15. Meaning: If AB  ED, AC  EF & BC  DF, then ΔABC  ΔEDF. ___ A BC E DF

16. Examples Let ABCD be a square and AC be one of its diagonals. What can you say about triangles ABC and CDA?

17. What additional information do you need to prove these are congruent by SSS?

18. Side-Angle-Side (SAS) If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, then the 2 triangles are congruent.

19. If BC  YX, AC  ZX, and  C   X, then ΔABC  ΔZXY. B A C X Y Z ) (

20. Examples Can you prove that the triangles below are congruent using SAS? 5 5 8 8

21. What additional information do you need to prove these are congruent by SAS?