Question

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.

Explanation:

Step1: Analyze Triangle #1

Triangle #1 has sides \(2.5\) cm, \(8\) cm, and \(6.75\) cm.

Step2: Analyze Triangle #3

Triangle #3 has sides \(2.5\) cm, \(6.75\) cm, and \(8\) cm.

Step3: Apply SSS Congruence Theorem

The SSS (Side - Side - Side) Congruence Theorem states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.
For Triangle #1 and Triangle #3, the three sides \(2.5\) cm, \(6.75\) cm, and \(8\) cm are equal.

Answer:

Triangle #1 and Triangle #3 are congruent.