Question

the sss congruence theorem practice
complete this assessment to review what youve learned. it will not count toward your grade.
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: Recall SSS Congruence Theorem

The SSS (Side - Side - Side) Congruence Theorem states that if the three sides of one triangle are equal in length to the three sides of another triangle, then the two triangles are congruent.

Step2: Analyze side - lengths of given triangles

Triangle #1 has side - lengths 2.5 cm, 8 cm, and 6.75 cm.
Triangle #2 is described by two sides (2.5 cm and 8 cm) and an included angle (60°), not by three side - lengths, so we can't use SSS on it.
Triangle #3 has two sides (2.5 cm and 6.75 cm) and an included angle (111.17°) and the third side of length 8 cm. The side - lengths of Triangle #1 are 2.5 cm, 8 cm, and 6.75 cm which match the side - lengths of Triangle #3.

Answer:

Triangle #1 and Triangle #3 are congruent.