4-2 Some ways to prove triangles Congruent

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

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

Proving Triangles Congruent Postulate 13 - 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

Proving Triangles Congruent Postulate 14 - 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

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

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

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

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

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

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

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

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