1. Section 4-2: Some Ways to Prove Triangles Congruent

2. C A B A B C B A C 𝐴𝐵 is opposite ∠_____
𝐴𝐵 is included between ∠_____ and ∠_____
𝐵𝐶 is opposite ∠_____
𝐵𝐶 is included between ∠_____ and ∠_____
𝐴𝐶 is opposite ∠_____
𝐴𝐶 is included between ∠_____ and ∠_____ A B A B C B A C

3. 𝐷𝐹 𝐷𝐹 𝐸𝐹 𝐸𝐹 𝐷𝐸 𝐷𝐸 _____ is opposite ∠E
_____ is included between ∠D and ∠F
_____ is opposite ∠D
_____ is included between ∠E and ∠F
_____ is opposite ∠F
_____ is included between ∠D and ∠E 𝐷𝐹 𝐸𝐹 𝐸𝐹 𝐷𝐸 𝐷𝐸

4. SSS Postulate: If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
∆____ ____ ____ ≅ ∆____ ____ ____ by ____ ____ ____
A B C F E D
S S S

5. SAS 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 triangles are congruent.
∆____ ____ ____ ≅ ∆____ ____ ____ by ____ ____ ____
A B C D F E
S A S

6. ASA Postulate: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
∆____ ____ ____ ≅ ∆____ ____ ____ by ____ ____ ____
A B C D F E
A S A

7. AAS Theorem: If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
∆____ ____ ____ ≅ ∆____ ____ ____ by ____ ____ ____
A B C D F E
A A S

8. HL Theorem: If the hypotenuse and a leg of one triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.
∆____ ____ ____ ≅ ∆____ ____ ____ by ____ ____
A B C D E F
H L

9. no congruence ∆ABC ≅ ∆DBC; SSS Examples:
Decide whether you can determine by the SSS, SAS, ASA, or AAS, whether the triangles are congruent. If so, write the congruence statement and name the postulate or theorem used. If not, write no congruence.
∆ABC ≅
∆DBC;
no congruence
SSS

10. no congruence
∆XYZ ≅
∆TUV;
SAS

11. ∆ABD ≅
∆CDB;
ASA
∆EFG ≅
∆IHG;
SAS

12. ∆JKN ≅
∆LMK;
SAS
∆PTS ≅
∆SRP;
SSS

13. ∆UVW ≅
∆UXW;
AAS
no congruence

14. ∆KML ≅
∆KMN;
∆ABC ≅
∆DEF; HL HL

15. ∆QPR ≅
∆STR;
no congruence
AAS

16. No congruence
∆ABC ≅
∆DEC;
SAS

17. 1. 𝐵𝐴 ⊥ 𝑌𝑍 ; 1. __________________
17. Supply the missing
statements & reasons.
Given: 𝐵𝐴 ⊥ 𝑌𝑍 ; 𝐵𝐴 bisects ∠YBZ.
Prove: ∆𝐴𝑌𝐵≅ ∆𝐴𝑍𝐵
STATEMENTS REASONS
1. 𝐵𝐴 ⊥ 𝑌𝑍 ; 1. __________________
2. ______ ≅ ________ 2. If two lines are perpendicular, then they form congruent
adjacent angles
3. __________________ 3. Given
4. ∠3 ≅ ∠ __________________
5. 𝐴𝐵 ≅ 𝐴𝐵 __________________
6. ______ ≅ ________ 6. ASA Postulate
Given
∠ ∠2
𝐵𝐴 bisects ∠YBZ
Def. of angle bisector
Reflexive Property
∆𝐴𝑌𝐵 ∆𝐴𝑍𝐵

18. HOWEWORK: page 124 #1-16 all