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
ot enough information\. explain your answer.
write a congruence statement and give a reason why the triangles are congruent. choose the correct answer below.
o a. △abc≅△def, sss
o b. △abc≅△def, sas
o c. the two triangles are not necessarily congruent. there is not enough information.

Explanation:

Step1: Recall the SSS and SAS congruence criteria

• SSS (Side - Side - Side) congruence: If three sides of one triangle are equal to the three corresponding sides of another triangle, then the two triangles are congruent.
• SAS (Side - Angle - Side) congruence: If two sides and the included angle of one triangle are equal to the two corresponding sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Analyze the given triangles

• For \(\triangle ABC\) and \(\triangle DEF\), we can see that two sides of \(\triangle ABC\) are equal to two sides of \(\triangle DEF\) (marked as equal in the figure), and the included angle of those two sides in \(\triangle ABC\) is equal to the included angle of the two corresponding sides in \(\triangle DEF\) (marked as equal in the figure).

Answer:

B. \(\triangle ABC\cong\triangle DEF\), SAS