Which of the following triangles are congruent by the SSS Congruence Theorem? Enter the lesser number first.

Triangle #1: a triangle with sides measuring 2.5 cm, 8 cm, and 6.75 cm in length

Triangle #2: a triangle with an angle measuring 60°
between sides measuring 2.5 cm and 8 cm in length

Triangle #3: a triangle with an angle measuring 111.17°
between sides measuring 2.5 cm and 6.75 cm in length, and a third side with a length of 8 cm

(1 point)
Triangle #
and Triangle #
are congruent.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
3 days ago

To determine if any of the given triangles are congruent by the SSS (Side-Side-Side) Congruence Theorem, we must compare the lengths of the sides of the triangles.

1. **Triangle #1** has sides measuring 2.5 cm, 6.75 cm, and 8 cm.
2. **Triangle #2** has two sides measuring 2.5 cm and 8 cm, but we do not know the length of the third side as it is defined by the angle (60°) between them. Therefore, we cannot match it to Triangle #1.
3. **Triangle #3** has sides measuring 2.5 cm, 6.75 cm, and 8 cm, but it is given in a different configuration (with an angle), so it does not directly provide the necessary information based on the third side.

Now checking for potential congruence:

- **Triangle #1** has side lengths: 2.5 cm, 6.75 cm, 8 cm.
- **Triangle #3** has sides that include a side of length 8 cm alongside sides of 2.5 cm and 6.75 cm as well.

Since Triangle #3 also has the sides 2.5 cm, 6.75 cm, and 8 cm, we can say:

**Triangle #1 and Triangle #3 are congruent by the SSS Congruence Theorem.**

Thus, the answer is:

Triangle 1 and Triangle 3 are congruent.