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The SAS Congruence Theorem Quick Check

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

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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1 answer

The SAS Congruence Theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle between those two sides is also congruent, then the two triangles are congruent.

To apply this theorem to your options, you need to look for a pair of triangles that show two pairs of congruent sides and one pair of congruent included angles (the angles formed by the two sides).

  1. The first option shows two congruent sides (EF and HI) and two congruent angles (F and I, E and H). However, it lacks the necessary included angle.

  2. The second option shows two pairs of congruent sides (FG and IJ, EF and HI) and the angle E is congruent to angle H (which is included between the two sides EF and HI), making it suitable for the SAS theorem.

  3. The third option has two pairs of congruent sides (EG and HJ, EF and HI), but again does not have the included angle explicitly stated to evaluate the SAS condition properly.

  4. The fourth option shows two pairs of congruent sides (FG and IJ, EF and HI) but lacks an included angle.

Based on the explanations, the second option is the correct answer as it satisfies all conditions of the SAS Congruence Theorem with the included angle being between the congruent sides.