Question

which postulate would prove the two triangle congruent?
sas
sss
asa
aas

Explanation:

Step1: Analyze the given sides

We can see that \(DA = DE\) (marked with two - cross), \(AT=ET\) (marked with one - cross), and \(DT = DT\) (common side).

Step2: Recall the congruence postulates

• SAS (Side - Angle - Side): Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
• SSS (Side - Side - Side): All three sides of one triangle are equal to all three sides of another triangle.
• ASA (Angle - Side - Angle): Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
• AAS (Angle - Angle - Side): Two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle.

Since we have three pairs of equal sides (\(DA = DE\), \(AT = ET\), \(DT=DT\)), we use the SSS postulate.

Answer:

SSS