Question

which congruency theorem can be used to prove that △abd ≅ △dca?
sas
sss
aas
asa

Explanation:

Step1: Analyze given sides and angles

From the figure, we can observe that \(AD = DA\) (common side), \(\angle ADB=\angle DAC = 90^{\circ}\), and \(AB = DC\) (given as marked).

Step2: Recall congruence theorems

• 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.
• 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.
• 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.

Here, we have two sides (\(AD = DA\) and \(AB = DC\)) and an included right angle (\(\angle ADB=\angle DAC\))

Answer:

SAS