Questions: What additional piece of information would you need to be able to state that triangle E F G is congruent to triangle H I J by the SSS Congruence Theorem?
Option #1: line segment H I is congruent to line segment I J
Option #2: line segment F G is congruent to line segment I J
Option #3: line segment G F is congruent to line segment H J
You would need the information in Option # to be able to state that triangle E F G is congruent to triangle H I J by the SSS Congruence Theorem.
Transcript text: What additional piece of information would you need to be able to state that $\triangle E F G \cong \triangle H I J$ by the SSS Congruence Theorem?
Option \#1: $\overline{H I} \cong \overline{I J}$
Option \#2: $\overline{F G} \cong \overline{I J}$
Option \#3: $\overline{G F} \cong \overline{H J}$
(1 point)
You would need the information in Option \# $\square$ to be able to state that $\triangle E F G \cong \triangle H I J$ by the SSS Congruence Theorem.
Check answer
Remaining Attempts : 3
Solution
Solution Steps
Step 1: Identify the Given Information
We are given two triangles, ΔEFG and ΔHIJ, and we need to determine what additional information is required to state that ΔEFG ≅ ΔHIJ by the SSS (Side-Side-Side) Congruence Theorem.
Step 2: Analyze the SSS Congruence Theorem
The SSS Congruence Theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
Step 3: Determine the Missing Information
We need to check which side congruence is missing to apply the SSS Congruence Theorem. From the given options:
Option #1: HI ≅ IJ
Option #2: FG ≅ IJ
Option #3: GF ≅ HJ
We need to find the option that completes the three pairs of congruent sides.
Final Answer
You would need the information in Option #3 (GF ≅ HJ) to be able to state that ΔEFG ≅ ΔHIJ by the SSS Congruence Theorem.