Question

triangle congruence by sss and sas
guided practice
what additional information is needed to prove by the sas postulate?
a. ∠abc ≅ ∠def
b. ∠cab ≅ ∠fde
c. ∠bca ≅ ∠efd

Explanation:

The SAS (Side - Angle - Side) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In the given triangles, we already know that \(AC = DF\) (from the tick marks). For SAS, we need the included angle between the sides. The sides \(AB\) and \(AC\) in \(\triangle ABC\) and \(DE\) and \(DF\) in \(\triangle DEF\) are considered. The included angle for \(AB\) and \(AC\) is \(\angle CAB\), and for \(DE\) and \(DF\) is \(\angle FDE\). So, we need \(\angle CAB\cong\angle FDE\).

Answer:

B. \(\angle CAB\cong\angle FDE\)