Which of the following pairs of triangles could you use to justify that the SAS Congruence Theorem is true?(1 point)

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An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side E F is congruent to side H I. Angle F is congruent to angle I. Angle E is congruent to angle H.
Image with alt text: An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side E F is congruent to side H I. Angle F is congruent to angle I. Angle E is congruent to angle H.

An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side F G is congruent to side I J. Side E F is congruent to side H I. Angle E is congruent to angle H.
Image with alt text: An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side F G is congruent to side I J. Side E F is congruent to side H I. Angle E is congruent to angle H.

An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side E G is congruent to side H J. Side E F is congruent to side H I. Angle E is congruent to angle H.
Image with alt text: An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side E G is congruent to side H J. Side E F is congruent to side H I. Angle E is congruent to angle H.

An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side F G is congruent to side I J. Side E F is congruent to side H I.
Image with alt text: An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side F G is congruent to side I J. Side E F is congruent to side H I.
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Answer 1

To justify the SAS (Side-Angle-Side) Congruence Theorem, you need a pair of triangles where two sides and the included angle between those sides are congruent.

Looking at the provided options:

1. Option 1: Side EF is congruent to side HI, angle F is congruent to angle I, and angle E is congruent to angle H.

   • This option has two angles and one side, which does not meet the criteria for SAS.

2. Option 2: Side FG is congruent to side IJ, side EF is congruent to side HI, and angle E is congruent to angle H.

   • This option has two sides and one angle, but the included angle is not clear here, so it does not fully justify SAS.

3. Option 3: Side EG is congruent to side HJ, side EF is congruent to side HI, and angle E is congruent to angle H.

   • This option has two sides and one angle, but again, the included angle is not explicitly shown.

4. Option 4: Side FG is congruent to side IJ, and side EF is congruent to side HI.

   • This option shows two sides, but omits any angle comparison.

Since none of the options provide a clear pairing of two sides with the included angle being congruent, it is difficult to determine if any of them justify the SAS Congruence Theorem completely. However, if we were to make an assumption based on what is typical, Option 2 might be the closest as it mentions two sides and an angle, but still fails to specify that the angle is the included one.

None of these seem to fully justify the SAS theorem effectively as presented, but Option 2 comes closest if we assume angle E is included between sides EF and FG.