Question

31 can you use the sss postulate or the sas postulate to prove \\( \triangle fez \cong \triangle fgz \\)? both apply by sas only by sss only neither apply

Explanation:

Step1: Identify common side

In \(\triangle FEZ\) and \(\triangle FGZ\), \(FZ = FZ\) (common side).

Step2: Check SSS

From the figure, \(FE=FG\) (marked with one - cross), \(EZ = GZ\) (marked with three - crosses), and \(FZ=FZ\). So, by SSS (Side - Side - Side) postulate (\(FE = FG\), \(EZ=GZ\), \(FZ = FZ\)), \(\triangle FEZ\cong\triangle FGZ\).

Step3: Check SAS

The included angle for \(FE\) and \(FZ\) in \(\triangle FEZ\) and \(FG\) and \(FZ\) in \(\triangle FGZ\) is the same (the angle at \(F\)). Also, \(FE = FG\), \(FZ=FZ\). So, by SAS (Side - Angle - Side) postulate (\(FE = FG\), \(\angle EFZ=\angle GFZ\), \(FZ = FZ\)), \(\triangle FEZ\cong\triangle FGZ\).

Answer:

both apply