Math 121

Section 3.1

Proving Congruent Triangles

Congruent Triangles

Two triangles are congruent when the six parts of one triangle are congruent to the corresponding six parts of the other triangle.

Correspondence in the two triangles

Methods of Proving Triangles Congruent

Postulate 12 (SSS)

IF three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

Postulate 13 (SAS)

If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.

Postulate 14 (ASA)

If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent.

Theorem 3.1.1 (AAS)

If two angles and a non-included side of one triangle are congruent to two angles and a non- included side of a second triangle, then the triangles are congruent.

Exercises

State what method would be used (SSS,AAS,ASA, or SAS)

9) SSS

11) AAS

14)

SAS

16)

SAS

22)

24)

Proofs

Page 118

27)

Statement	Reason
1)	1) Given
2)	2) Definition of a bisector
3)	3) Identity Property
4)	4) SAS

28)

Statement	Reason
1)	1) Given
2)	2) Definition of perpendicular lines
3)	3) All right angles are congruent
4)	4) Identity Property
5)	5) SAS

30)

Statements	Reason
1)	1) Given
2)	2) All right angles are congruent
3)	3) Definition of a bisector
4)	4) If two lines intersect, the vertical angles form are congruent
5)	5) ASA

1)

Statement	Reason
1)	1) Given
2)	2) Identity Property
3)	3) SSS

2)

Statement	Reason
1)	1) Given
2)	2) Identity Property
3)	3) ASA