Question

would you use sss or sas to prove the triangles congruent? use only the marked sides/angles and any shared sides. if there is not enough information to prove the triangles congruent by sss or sas, write not enough information. explain your answer. write a congruence statement and give a reason why the triangles are congruent. choose the correct answer below. a. △arc≅△det, sss b. △arc≅△det, sas c. the two triangles are not necessarily congruent. there is not enough information.

Explanation:

Step1: Check SAS condition

In SAS (Side - Angle - Side) congruence, two sides and the included angle of one triangle must be equal to two sides and the included angle of another triangle.
For \(\triangle ARC\) and \(\triangle DET\), we have two pairs of equal sides (marked as equal in the figure) and the included angles (marked angles) between those sides.

Step2: Verify congruence

Since two sides and the included angle of \(\triangle ARC\) are equal to two sides and the included angle of \(\triangle DET\), by the SAS (Side - Angle - Side) congruence criterion, \(\triangle ARC\cong\triangle DET\).

Answer:

B. \(\triangle ARC\cong\triangle DET\), SAS