Question

Can you use the ASA Postulate or the AAS Theorem to prove the triangles congruent?

Answer 1

ASA only

Explanation:

We are given that two triangles in which

An angle of triangle is equal to its corresponding angle of second triangle.

One side of a triangle is equal to one side of other triangle.

ASA postulate: It states that two angles and included side of one triangle are congruent to its corresponding angles and corresponding side of other triangle , then the two triangles are congruent.

AAS postulate: It states that two angles and non- included side of one triangle are congruent to its corresponding two angles and its corresponding side of another triangle, then the triangles are congruent by AAS postulate.

In triangle AOB and COD

`\angle AOB= \angle COD` (Vertical angles are equal )

`\angle ABO=\angle CDO` ( Given )

`OB=OD` (Given )

`\triangle AOB\cong \triangle COD` ( ASA Postulate )

Answer: ASA only

Answer 2

ASA only

Explanation:

Given is a picture of two triangles with one side and one angle congruent.

Comparison of these two triangles given

side = side

one angle = one angle (given)

Second angle = second angle (Vertically opposite angles)

Thus we find here that two angles and one corresponding side are congruent.

HEnce we say that these two triangles are congruent by ASA theorem

ASA theorem can be applied here because the equal side is between the two congruent angles.

Instead if the side is not between the congruent angles but corresponding side then we can only use AAS

SO here ASA is correct.