1. Congruent Triangles Unit 4-5 Congruent Triangle Theorems

2. Rules to prove triangles are = Side-Side-Side-- Each side is equal to its corresponding side on the 2 nd triangle. M P T R Q K

3. Rules to prove triangles are = Side-Angle-Side-- Two sides and the included angle on one triangle are equal to the corresponding sides and angle on the 2 nd triangle. A N H B D R

4. Rules to prove triangles are = Angle-Side-Angle-- Two angles and the included sides on one triangle are equal to the corresponding angles and side on the 2 nd triangle. A N H B D R

5. Rules to prove triangles are = Angle-Angle-Side-- Two angles and the excluded sides on one triangle are equal to the corresponding angles and side on the 2 nd triangle. A N H B D R

6. Rules to prove triangles are = HL -- On Right Triangles ONLY! The corresponding Hypotenuse and a leg are equal. A N H B D R

7. Rules to prove triangles are = CPCTC Corresponding parts of congruent triangle are congruent. A N H B D R Are these triangle =? Why? SAS Then…. All other corresponding parts are = as well By the rule CPCTC

8. Examples—are the triangles = Are they equal? If so, why!!! Are they equal? WHY??? Statement of congruence A B C D F G

9. Examples—are the triangles = Are they equal? If so, why!!! Are they equal? Yes WHY??? ASA A B C D F G Statement of Congruence ΔAGC = ΔFDB

10. Examples—are the triangles = Are they equal? If so, why!!! Are they equal? WHY??? A BC D F G Statement of Congruence

11. Examples—are the triangles = Are they equal? If so, why!!! Are they equal? WHY??? A B C D F G Statement of Congruence

12. Examples—are the triangles = Are they equal? If so, why!!! Are they equal? WHY??? A B C D F G Statement of Congruence

13. Examples—are the triangles = Are they equal? If so, why!!! Are they equal? WHY??? A B C D F G Statement of Congruence

14. Examples—are the triangles = Are they equal? If so, why!!! Are they equal? WHY??? A B C D F G Statement of Congruence

15. Use corresponding parts of congruent triangles (21.6) o (6x – 12) o  Find the value of x  Find m GFH Given: E F G H

16. Find the value of x and y. Then find all missing measures A B C T R S 100 o 4x - 2 3x + 8 (y – 5) o (2y – 10) o m A = ________ m B = _________ m C = ________ m S = ________ m T = _________ m R = ________ AC = __________ AB = _________ RS = ___________ TS = _________