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

Answer 1

To use the Side-Angle-Side (SAS) Congruence Theorem, you need to have two sides of one triangle that are congruent to two sides of another triangle, and the included angle between those two sides must also be congruent.

Let's analyze the provided responses:

1. First image:

   • Side \(EG \cong HJ\)
   • Side \(EF \cong HI\)
   • Angle \(E \cong H\)
   • This configuration has two sides congruent and the angle between them congruent. This can justify the SAS theorem.

2. Second image:

   • Side \(FG \cong IJ\)
   • Side \(EF \cong HI\)
   • No angle is included between the two congruent sides. This does not satisfy SAS.

3. Third image:

   • Side \(FG \cong IJ\)
   • Side \(EF \cong HI\)
   • Angle \(E \cong H\)
   • Similar to the second, the included angle isn't between the two congruent sides, so it does not satisfy SAS.

4. Fourth image:

   • Side \(EF \cong HI\)
   • Angle \(F \cong I\)
   • Angle \(E \cong H\)
   • There are no sides involved in this selection, so it does not satisfy SAS.

The correct choice to justify the SAS Congruence Theorem is the first image, where the two sides and the included angle are congruent.

Answer 2

are you SURE

Answer 3

Yes, I'm sure. Let's go over it again specifically for the SAS (Side-Angle-Side) Congruence Theorem:

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

In this light, we analyze again:

1. First image:

   • Side \(EG \cong HJ\) (one pair of sides)
   • Side \(EF \cong HI\) (second pair of sides)
   • Angle \(E \cong H\) (included angle between the two sides)
   • This configuration satisfies the conditions of the SAS theorem.

2. Second image:

   • Side \(FG \cong IJ\)
   • Side \(EF \cong HI\)
   • No included angle between the two sides that are congruent. So, it does not satisfy the SAS theorem.

3. Third image:

   • Side \(FG \cong IJ\)
   • Side \(EF \cong HI\)
   • Angle \(E \cong H\)
   • Again, there's no angle between the two sides. Thus, it does not satisfy SAS.

4. Fourth image:

   • Side \(EF \cong HI\)
   • Angle \(F \cong I\) and Angle \(E \cong H\)
   • This choice involves no sides that are compared, and thus it also does not satisfy the SAS theorem.

Therefore, the first image is indeed the correct choice for demonstrating the SAS Congruence Theorem. If you have any further questions or need more clarification, feel free to ask!