Question

13
is $\triangle abc \cong \triangle def$? if so, name the postulate that applies.
given;
$\overline{ab} \cong \overline{de}$
$\overline{bc} \cong \overline{ef}$
$\angle b \cong \angle e$
a. congruent - asa
b. congruent - sas
c. might not be congruent
d. congruent - sss

Explanation:

Step1: Recall Congruence Postulates

• SAS (Side - Angle - Side) postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
• ASA (Angle - Side - Angle): Two angles and the included side.
• SSS (Side - Side - Side): Three sides.

Step2: Analyze Given Information

• We are given \(AB\cong DE\), \(BC\cong EF\), and \(\angle B\cong\angle E\).
• In \(\triangle ABC\) and \(\triangle DEF\), side \(AB\) and side \(BC\) with included angle \(\angle B\) in \(\triangle ABC\); side \(DE\) and side \(EF\) with included angle \(\angle E\) in \(\triangle DEF\) are congruent. This matches the SAS postulate.

Answer:

B. Congruent - SAS