Question

What additional information would he need to prove the triangles are congruent using the Side-Angle-Side method?

Answer 1

`\angle A \cong \angle D`

Explanation:

Two ∆s can be considered to be congruent to each other using the Side-Angle-Side Congruence Theorem, if an included angle, and two sides of a ∆ are congruent to an included angle and two corresponding sides of another ∆.

∆ABC and ∆DEF has been drawn as shown in the attachment below.

We are given that
`\overline{AB} \cong \overline{DE}` and also
`\overline{AC} \cong \overline{DF}`.

In order to prove that ∆ABC
`\cong` ∆DEF using the Side-Angle-Side Congruence Theorem, an included angle which lies between two known side must be made know in each given ∆s, which must be congruent accordingly to each other.

The included angle has been shown in the ∆s drawn in the diagram attached below.

Therefore, the additional information that would be need is:

`\angle A \cong \angle D`