Question

In addition to the facts in the diagram, which other statements are necessary to prove that ?abc is congruent to ?efg by the ASA criterion?

1) i and iii only
2) i or iv only
3) i only
4) iii or v only

Answer 1

The correct answer is 3) i only. Only the information provided in statement i, in addition to the facts in the diagram, is necessary to prove that \(\triangle ABC\) is congruent to \(\triangle EFG\) by the ASA criterion.

Step-by-step explanation:

To prove that
`\(\triangle ABC\)` is congruent to
`\(\triangle EFG\)` using the ASA (Angle-Side-Angle) criterion, we need to establish the following:

i) Angle A is congruent to Angle E: This is the ASA criterion, where two angles and the included side are equal in both triangles.

The other statements (ii, iii, iv, and v) are not necessary for proving congruence using the ASA criterion. For instance, statement iii provides information about the sides being equal, which is not required for the ASA criterion. Similarly, statements iv and v involve information about angles or sides that are not part of the congruent criteria in ASA.

It's crucial to recognize that the ASA criterion only requires the equality of two angles and the included side. Therefore, statement i alone, which asserts that angle A is congruent to angle E, is sufficient to prove congruence between
`\(\triangle ABC\)` and
`\(\triangle EFG\)` under the ASA criterion.

In summary, the necessary information to prove congruence by the ASA criterion is provided in statement i alone, making option 3) i only the correct answer.

Answer 2

1

Step-by-step explanation:

a side was given and you needed two angles to be congruent