1. 4-2 Some ways to prove triangles Congruent

2. Proving Triangle congruent
If two triangles are congruent, the six parts of one triangle are congruent to the six corresponding parts of the other triangle. If you are not sure whether two triangles are congruent, it is NOT necessary to compare all six pairs. Three pairs of corresponding parts will guarantee that two triangles are congruent.
Postulate 12- SSS postulate
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. E G Y B 5 5 3 3 A C F H P R 4 T O 4

3. Proving Triangles Congruent
Sometimes it is helpful to describe the parts of the triangle in terms of their relative positions.
AB is opposite < c
AB is included between < A and < B
< A is opposite BC
< A is included between AB and AC B A C

4. Proving Triangles Congruent
Postulate 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 SAS postulate, ABC = FGH and MEL = ODY L O 3 9 E 60 60 D 3 9 M Y

5. Proving Triangles Congruent
Postulate 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 the ASA Postulate ABC = FGH MON = KEY K B H M 4 4 Y 55 55 N A C F G O E

6. Proving Triangles Congruent
Given: E is the midpoint of MJ;
TE MJ
Prove: MET = JET M J E
Statements
Reasons
E is the midpoint of of MJ
TE JE
< MET = < JET
TE = ________
MET = JET

7. Proving Triangles Congruent
Given: E is the midpoint of MJ;
TE MJ
Prove: MET = JET M J E
Statements
Reasons
E is the midpoint of of MJ
Given
Def. of Midpoint
TE JE
< MET = < JET
TE = ________
MET = JET

8. Proving Triangles Congruent
Given: E is the midpoint of MJ;
TE MJ
Prove: MET = JET M J E
Statements
Reasons
E is the midpoint of of MJ
Given
ME = JE
Def. of Midpoint
TE JE
< MET = < JET
TE = ________
MET = JET

9. Proving Triangles Congruent
Given: E is the midpoint of MJ;
TE MJ
Prove: MET = JET M J E
Statements
Reasons
E is the midpoint of of MJ
Given
ME = JE
Def. of Midpoint
TE JE
< MET = < JET
TE = ________
MET = JET

10. Proving Triangles Congruent
Given: E is the midpoint of MJ;
TE MJ
Prove: MET = JET M J E
Statements
Reasons
E is the midpoint of of MJ
Given
ME = JE
Def. of Midpoint
TE JE
< MET = < JET
Perpendicular lines form congruent adjacent angles
TE = ________
MET = JET

11. Proving Triangles Congruent
Given: E is the midpoint of MJ;
TE MJ
Prove: MET = JET M J E
Statements
Reasons
E is the midpoint of of MJ
Given
ME = JE
Def. of Midpoint
TE JE
< MET = < JET
Perpendicular lines form congruent adjacent angles
TE = __TE _
MET = JET

12. Proving Triangles Congruent
Given: E is the midpoint of MJ;
TE MJ
Prove: MET = JET M J E
Statements
Reasons
E is the midpoint of of MJ
Given
ME = JE
Def. of Midpoint
TE JE
< MET = < JET
Perpendicular lines form congruent adjacent angles
TE = __TE _
Reflexive
MET = JET

13. Proving Triangles Congruent
Given: E is the midpoint of MJ;
TE MJ
Prove: MET = JET M J E
Statements
Reasons
E is the midpoint of of MJ
Given
ME = JE
Def. of Midpoint
TE JE
< MET = < JET
Perpendicular lines form congruent adjacent angles
TE = __TE _
Reflexive
MET = JET
SAS Postulate