Question

Which postulate or theorem proves that these two triangles are congruent?

1) SAS Congruence Postulate
2) ASA Congruence Postulate
3) AAS Congruence Theorem
4) HL Congruence Theorem

Answer 1

The postulate or theorem that proves that two triangles are congruent in this case is the SAS Congruence Postulate.

Step-by-step explanation:

The postulate or theorem that proves that two triangles are congruent in this case is the SAS Congruence Postulate. SAS stands for 'side-angle-side'. According to this postulate, if two triangles have one pair of corresponding sides that are congruent, and the angles formed by those sides are congruent, then the triangles are congruent.

For example, if Triangle ABC has side AB congruent to side DE, side BC congruent to side EF, and angle ABC congruent to angle DEF, then triangle ABC is congruent to triangle DEF by the SAS Congruence Postulate.

Therefore, in this case, the SAS Congruence Postulate can be used to prove that the two triangles are congruent.