In the figure shown, what additional information is needed to show that △ABC≅△DEF by SSS?

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Answer:

Step-by-step explanation:

They're asking for what other information is needed.

We were given triangle ABC is congruent to triangle DEF. We know for certain line AB and line DC are congruent to each other as well as lines BC and EF.

The additional information we need to know is if line AC is congruent to line DF to absolutely be sure.

Remember SSS by definition is:  Triangles are congruent if all three sides in one triangle are congruent to the corresponding sides in the other. If all three sides in one triangle are the same length as the corresponding sides in the other, then the triangles are congruent.

SSS congruence of triangles is proved when all three sides of considered two triangles are congruent(that is, of equal measures).

Thus, the needed answer is:

Line segment DF is congruent to line segment AC

or [tex]\overline{DF} \cong \overline{AC}[/tex]

If two considered triangles have corresponding side pairs congruent(for all three sides), then both the triangles are congruent. This proof of congruence is triangle is done by SSS congruence of triangles (Side Side Side congruence)

Since it is given that the sides CB and FE are congruent,

and since it is given that sides AB and DE are congruent too,

thus, for SSS congruence of both considered triangles, we need the third side pair of the given triangles to be congruent too.

Thus, we need the line segment DF congruent to the line segment AC.

We can write it symbolically as:

[tex]\overline{DF} \cong \overline{AC}[/tex] (remember that order doesn't matter here. You could've written [tex]\overline{AC} \cong \overline{DF}[/tex] too.)

Learn more about SSS congruence of triangles here:

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