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. ( \triangle abocong\triangle det ), sss
b. ( \triangle abocong\triangle det ), sas
c. the two triangles are not necessarily congruent. there is not enough information

Explanation:

Step1: Recall SAS and SSS criteria

SAS (Side - Angle - Side) criterion: Two sides and the included angle of one triangle are equal to the corresponding two sides and the included angle of another triangle.
SSS (Side - Side - Side) criterion: All three sides of one triangle are equal to the corresponding three sides of another triangle.

Step2: Analyze the given triangles

In \(\triangle ABO\) and \(\triangle DET\), we have two pairs of equal sides (marked with ticks) and one pair of equal angles. The equal angle is between the two equal sides (by the way the sides and angles are marked in the figure).

Step3: Apply the congruence criterion

Since we have two sides and the included angle equal, we use the SAS (Side - Angle - Side) congruence criterion.

Answer:

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