An illustration shows two congruent triangles in different orientations. Two corresponding sides are marked as congruent.

Question

What additional piece of information would you need to be able to state that △EFG≅△HIJ
by the SSS Congruence Theorem?

Option #1: HI¯¯¯¯¯¯¯≅IJ¯¯¯¯¯¯


Option #2: FG¯¯¯¯¯¯¯¯≅IJ¯¯¯¯¯¯


Option #3: GF¯¯¯¯¯¯¯¯≅HJ¯¯¯¯¯¯¯¯


(1 point)
You would need the information in Option #
to be able to state that ​△EFG≅△HIJ
by the SSS Congruence Theorem.

Answer 1

To use the Side-Side-Side (SSS) Congruence Theorem, you need to have the lengths of all three sides of each triangle to prove that they are congruent. Since two sides of triangles EFG and HIJ are already marked as congruent, you need information about the lengths of the third sides.

Since the options provided are about the congruency of sides, we need to find which option gives us the congruency of one of the remaining sides in triangle HIJ.

1. Option #1: HI ≅ IJ: This does not help, as it does not involve any sides from triangle EFG.

2. Option #2: FG ≅ IJ: This provides a congruency statement, but it is between one side from EFG and one from HIJ.

3. Option #3: GF ≅ HJ: This option gives congruency information about another side that involves one side from triangle EFG and one from triangle HIJ.

Since to prove triangles congruent using SSS, we need to know all corresponding sides, Option #3 provides the necessary information linking the remaining sides of both triangles.

Thus, you would need the information in Option #3 to be able to state that ​△EFG ≅ △HIJ by the SSS Congruence Theorem.